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<li>
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<a class="reference reference-toplevel" href="#6" id="56">Imports</a>
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</li>
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<li>
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<details open>
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<summary><a class="reference reference-toplevel" href="#7" id="57">Types</a></summary>
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<ul class="simple simple-toc-section">
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<li><a class="reference" href="#Complex" title="Complex[T] = object
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re*, im*: T">Complex</a></li>
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<li><a class="reference" href="#Complex32" title="Complex32 = Complex[float32]">Complex32</a></li>
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<li><a class="reference" href="#Complex64" title="Complex64 = Complex[float64]">Complex64</a></li>
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</ul>
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</details>
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</li>
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<li>
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<details open>
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<summary><a class="reference reference-toplevel" href="#12" id="62">Procs</a></summary>
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<ul class="simple simple-toc-section">
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<ul class="simple nested-toc-section">$
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<li><a class="reference" href="#%24%2CComplex" title="`$`(z: Complex): string">`$`(z: Complex): string</a></li>
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</ul>
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<ul class="simple nested-toc-section">*
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<li><a class="reference" href="#%2A%2CComplex%5BT%5D%2CComplex%5BT%5D" title="`*`[T](x, y: Complex[T]): Complex[T]">`*`[T](x, y: Complex[T]): Complex[T]</a></li>
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<li><a class="reference" href="#%2A%2CComplex%5BT%5D%2CT" title="`*`[T](x: Complex[T]; y: T): Complex[T]">`*`[T](x: Complex[T]; y: T): Complex[T]</a></li>
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<li><a class="reference" href="#%2A%2CT%2CComplex%5BT%5D" title="`*`[T](x: T; y: Complex[T]): Complex[T]">`*`[T](x: T; y: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">*=
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<li><a class="reference" href="#%2A%3D%2CComplex%5BT%5D%2CComplex%5BT%5D" title="`*=`[T](x: var Complex[T]; y: Complex[T])">`*=`[T](x: var Complex[T]; y: Complex[T])</a></li>
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</ul>
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<ul class="simple nested-toc-section">+
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<li><a class="reference" href="#%2B%2CComplex%5BT%5D%2CComplex%5BT%5D" title="`+`[T](x, y: Complex[T]): Complex[T]">`+`[T](x, y: Complex[T]): Complex[T]</a></li>
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<li><a class="reference" href="#%2B%2CComplex%5BT%5D%2CT" title="`+`[T](x: Complex[T]; y: T): Complex[T]">`+`[T](x: Complex[T]; y: T): Complex[T]</a></li>
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<li><a class="reference" href="#%2B%2CT%2CComplex%5BT%5D" title="`+`[T](x: T; y: Complex[T]): Complex[T]">`+`[T](x: T; y: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">+=
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<li><a class="reference" href="#%2B%3D%2CComplex%5BT%5D%2CComplex%5BT%5D" title="`+=`[T](x: var Complex[T]; y: Complex[T])">`+=`[T](x: var Complex[T]; y: Complex[T])</a></li>
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</ul>
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<ul class="simple nested-toc-section">-
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<li><a class="reference" href="#-%2CComplex%5BT%5D%2CComplex%5BT%5D" title="`-`[T](x, y: Complex[T]): Complex[T]">`-`[T](x, y: Complex[T]): Complex[T]</a></li>
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<li><a class="reference" href="#-%2CComplex%5BT%5D%2CT" title="`-`[T](x: Complex[T]; y: T): Complex[T]">`-`[T](x: Complex[T]; y: T): Complex[T]</a></li>
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<li><a class="reference" href="#-%2CT%2CComplex%5BT%5D" title="`-`[T](x: T; y: Complex[T]): Complex[T]">`-`[T](x: T; y: Complex[T]): Complex[T]</a></li>
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<li><a class="reference" href="#-%2CComplex%5BT%5D" title="`-`[T](z: Complex[T]): Complex[T]">`-`[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">-=
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<li><a class="reference" href="#-%3D%2CComplex%5BT%5D%2CComplex%5BT%5D" title="`-=`[T](x: var Complex[T]; y: Complex[T])">`-=`[T](x: var Complex[T]; y: Complex[T])</a></li>
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</ul>
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<ul class="simple nested-toc-section">/
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<li><a class="reference" href="#%2F%2CComplex%5BT%5D%2CComplex%5BT%5D" title="`/`[T](x, y: Complex[T]): Complex[T]">`/`[T](x, y: Complex[T]): Complex[T]</a></li>
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<li><a class="reference" href="#%2F%2CComplex%5BT%5D%2CT" title="`/`[T](x: Complex[T]; y: T): Complex[T]">`/`[T](x: Complex[T]; y: T): Complex[T]</a></li>
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<li><a class="reference" href="#%2F%2CT%2CComplex%5BT%5D" title="`/`[T](x: T; y: Complex[T]): Complex[T]">`/`[T](x: T; y: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">/=
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<li><a class="reference" href="#%2F%3D%2CComplex%5BT%5D%2CComplex%5BT%5D" title="`/=`[T](x: var Complex[T]; y: Complex[T])">`/=`[T](x: var Complex[T]; y: Complex[T])</a></li>
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</ul>
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<ul class="simple nested-toc-section">==
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<li><a class="reference" href="#%3D%3D%2CComplex%5BT%5D%2CComplex%5BT%5D" title="`==`[T](x, y: Complex[T]): bool">`==`[T](x, y: Complex[T]): bool</a></li>
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</ul>
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<ul class="simple nested-toc-section">abs
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<li><a class="reference" href="#abs%2CComplex%5BT%5D" title="abs[T](z: Complex[T]): T">abs[T](z: Complex[T]): T</a></li>
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</ul>
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<ul class="simple nested-toc-section">abs2
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<li><a class="reference" href="#abs2%2CComplex%5BT%5D" title="abs2[T](z: Complex[T]): T">abs2[T](z: Complex[T]): T</a></li>
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</ul>
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<ul class="simple nested-toc-section">almostEqual
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<li><a class="reference" href="#almostEqual%2CComplex%5BT%3A%20SomeFloat%5D%2CComplex%5BT%3A%20SomeFloat%5D%2CNatural" title="almostEqual[T: SomeFloat](x, y: Complex[T]; unitsInLastPlace: Natural = 4): bool">almostEqual[T: SomeFloat](x, y: Complex[T]; unitsInLastPlace: Natural = 4): bool</a></li>
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</ul>
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<ul class="simple nested-toc-section">arccos
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<li><a class="reference" href="#arccos%2CComplex%5BT%5D" title="arccos[T](z: Complex[T]): Complex[T]">arccos[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">arccosh
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<li><a class="reference" href="#arccosh%2CComplex%5BT%5D" title="arccosh[T](z: Complex[T]): Complex[T]">arccosh[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">arccot
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<li><a class="reference" href="#arccot%2CComplex%5BT%5D" title="arccot[T](z: Complex[T]): Complex[T]">arccot[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">arccoth
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<li><a class="reference" href="#arccoth%2CComplex%5BT%5D" title="arccoth[T](z: Complex[T]): Complex[T]">arccoth[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">arccsc
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<li><a class="reference" href="#arccsc%2CComplex%5BT%5D" title="arccsc[T](z: Complex[T]): Complex[T]">arccsc[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">arccsch
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<li><a class="reference" href="#arccsch%2CComplex%5BT%5D" title="arccsch[T](z: Complex[T]): Complex[T]">arccsch[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">arcsec
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<li><a class="reference" href="#arcsec%2CComplex%5BT%5D" title="arcsec[T](z: Complex[T]): Complex[T]">arcsec[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">arcsech
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<li><a class="reference" href="#arcsech%2CComplex%5BT%5D" title="arcsech[T](z: Complex[T]): Complex[T]">arcsech[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">arcsin
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<li><a class="reference" href="#arcsin%2CComplex%5BT%5D" title="arcsin[T](z: Complex[T]): Complex[T]">arcsin[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">arcsinh
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<li><a class="reference" href="#arcsinh%2CComplex%5BT%5D" title="arcsinh[T](z: Complex[T]): Complex[T]">arcsinh[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">arctan
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<li><a class="reference" href="#arctan%2CComplex%5BT%5D" title="arctan[T](z: Complex[T]): Complex[T]">arctan[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">arctanh
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<li><a class="reference" href="#arctanh%2CComplex%5BT%5D" title="arctanh[T](z: Complex[T]): Complex[T]">arctanh[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">complex
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<li><a class="reference" href="#complex%2CT%2CT" title="complex[T: SomeFloat](re: T; im: T = 0.0): Complex[T]">complex[T: SomeFloat](re: T; im: T = 0.0): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">complex32
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<li><a class="reference" href="#complex32%2Cfloat32%2Cfloat32" title="complex32(re: float32; im: float32 = 0.0): Complex32">complex32(re: float32; im: float32 = 0.0): Complex32</a></li>
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</ul>
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<ul class="simple nested-toc-section">complex64
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<li><a class="reference" href="#complex64%2Cfloat64%2Cfloat64" title="complex64(re: float64; im: float64 = 0.0): Complex64">complex64(re: float64; im: float64 = 0.0): Complex64</a></li>
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</ul>
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<ul class="simple nested-toc-section">conjugate
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<li><a class="reference" href="#conjugate%2CComplex%5BT%5D" title="conjugate[T](z: Complex[T]): Complex[T]">conjugate[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">cos
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<li><a class="reference" href="#cos%2CComplex%5BT%5D" title="cos[T](z: Complex[T]): Complex[T]">cos[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">cosh
|
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<li><a class="reference" href="#cosh%2CComplex%5BT%5D" title="cosh[T](z: Complex[T]): Complex[T]">cosh[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">cot
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<li><a class="reference" href="#cot%2CComplex%5BT%5D" title="cot[T](z: Complex[T]): Complex[T]">cot[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">coth
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<li><a class="reference" href="#coth%2CComplex%5BT%5D" title="coth[T](z: Complex[T]): Complex[T]">coth[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">csc
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<li><a class="reference" href="#csc%2CComplex%5BT%5D" title="csc[T](z: Complex[T]): Complex[T]">csc[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">csch
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|
<li><a class="reference" href="#csch%2CComplex%5BT%5D" title="csch[T](z: Complex[T]): Complex[T]">csch[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">exp
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<li><a class="reference" href="#exp%2CComplex%5BT%5D" title="exp[T](z: Complex[T]): Complex[T]">exp[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">formatValue
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<li><a class="reference" href="#formatValue%2Cstring%2CComplex%2Cstring" title="formatValue(result: var string; value: Complex; specifier: string)">formatValue(result: var string; value: Complex; specifier: string)</a></li>
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</ul>
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<ul class="simple nested-toc-section">inv
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<li><a class="reference" href="#inv%2CComplex%5BT%5D" title="inv[T](z: Complex[T]): Complex[T]">inv[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">ln
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<li><a class="reference" href="#ln%2CComplex%5BT%5D" title="ln[T](z: Complex[T]): Complex[T]">ln[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
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<ul class="simple nested-toc-section">log2
|
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<li><a class="reference" href="#log2%2CComplex%5BT%5D" title="log2[T](z: Complex[T]): Complex[T]">log2[T](z: Complex[T]): Complex[T]</a></li>
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|
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|
</ul>
|
|
<ul class="simple nested-toc-section">log10
|
|
<li><a class="reference" href="#log10%2CComplex%5BT%5D" title="log10[T](z: Complex[T]): Complex[T]">log10[T](z: Complex[T]): Complex[T]</a></li>
|
|
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</ul>
|
|
<ul class="simple nested-toc-section">phase
|
|
<li><a class="reference" href="#phase%2CComplex%5BT%5D" title="phase[T](z: Complex[T]): T">phase[T](z: Complex[T]): T</a></li>
|
|
|
|
</ul>
|
|
<ul class="simple nested-toc-section">polar
|
|
<li><a class="reference" href="#polar%2CComplex%5BT%5D" title="polar[T](z: Complex[T]): tuple[r, phi: T]">polar[T](z: Complex[T]): tuple[r, phi: T]</a></li>
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|
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|
</ul>
|
|
<ul class="simple nested-toc-section">pow
|
|
<li><a class="reference" href="#pow%2CComplex%5BT%5D%2CComplex%5BT%5D" title="pow[T](x, y: Complex[T]): Complex[T]">pow[T](x, y: Complex[T]): Complex[T]</a></li>
|
|
<li><a class="reference" href="#pow%2CComplex%5BT%5D%2CT" title="pow[T](x: Complex[T]; y: T): Complex[T]">pow[T](x: Complex[T]; y: T): Complex[T]</a></li>
|
|
|
|
</ul>
|
|
<ul class="simple nested-toc-section">rect
|
|
<li><a class="reference" href="#rect%2CT%2CT" title="rect[T](r, phi: T): Complex[T]">rect[T](r, phi: T): Complex[T]</a></li>
|
|
|
|
</ul>
|
|
<ul class="simple nested-toc-section">sec
|
|
<li><a class="reference" href="#sec%2CComplex%5BT%5D" title="sec[T](z: Complex[T]): Complex[T]">sec[T](z: Complex[T]): Complex[T]</a></li>
|
|
|
|
</ul>
|
|
<ul class="simple nested-toc-section">sech
|
|
<li><a class="reference" href="#sech%2CComplex%5BT%5D" title="sech[T](z: Complex[T]): Complex[T]">sech[T](z: Complex[T]): Complex[T]</a></li>
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</ul>
|
|
<ul class="simple nested-toc-section">sgn
|
|
<li><a class="reference" href="#sgn%2CComplex%5BT%5D" title="sgn[T](z: Complex[T]): Complex[T]">sgn[T](z: Complex[T]): Complex[T]</a></li>
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|
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</ul>
|
|
<ul class="simple nested-toc-section">sin
|
|
<li><a class="reference" href="#sin%2CComplex%5BT%5D" title="sin[T](z: Complex[T]): Complex[T]">sin[T](z: Complex[T]): Complex[T]</a></li>
|
|
|
|
</ul>
|
|
<ul class="simple nested-toc-section">sinh
|
|
<li><a class="reference" href="#sinh%2CComplex%5BT%5D" title="sinh[T](z: Complex[T]): Complex[T]">sinh[T](z: Complex[T]): Complex[T]</a></li>
|
|
|
|
</ul>
|
|
<ul class="simple nested-toc-section">sqrt
|
|
<li><a class="reference" href="#sqrt%2CComplex%5BT%5D" title="sqrt[T](z: Complex[T]): Complex[T]">sqrt[T](z: Complex[T]): Complex[T]</a></li>
|
|
|
|
</ul>
|
|
<ul class="simple nested-toc-section">tan
|
|
<li><a class="reference" href="#tan%2CComplex%5BT%5D" title="tan[T](z: Complex[T]): Complex[T]">tan[T](z: Complex[T]): Complex[T]</a></li>
|
|
|
|
</ul>
|
|
<ul class="simple nested-toc-section">tanh
|
|
<li><a class="reference" href="#tanh%2CComplex%5BT%5D" title="tanh[T](z: Complex[T]): Complex[T]">tanh[T](z: Complex[T]): Complex[T]</a></li>
|
|
|
|
</ul>
|
|
|
|
</ul>
|
|
</details>
|
|
</li>
|
|
<li>
|
|
<details open>
|
|
<summary><a class="reference reference-toplevel" href="#18" id="68">Templates</a></summary>
|
|
<ul class="simple simple-toc-section">
|
|
<ul class="simple nested-toc-section">im
|
|
<li><a class="reference" href="#im.t%2Cfloat32" title="im(arg: float32): Complex32">im(arg: float32): Complex32</a></li>
|
|
<li><a class="reference" href="#im.t%2Cfloat64" title="im(arg: float64): Complex64">im(arg: float64): Complex64</a></li>
|
|
<li><a class="reference" href="#im.t%2Ctypedesc%5Bfloat32%5D" title="im(arg: typedesc[float32]): Complex32">im(arg: typedesc[float32]): Complex32</a></li>
|
|
<li><a class="reference" href="#im.t%2Ctypedesc%5Bfloat64%5D" title="im(arg: typedesc[float64]): Complex64">im(arg: typedesc[float64]): Complex64</a></li>
|
|
|
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</ul>
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|
</ul>
|
|
</details>
|
|
</li>
|
|
|
|
</ul>
|
|
|
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</div>
|
|
<div class="nine columns" id="content">
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L1" class="link-seesrc" target="_blank">Source</a>
|
|
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L1" class="link-seesrc" target="_blank" >Edit</a>
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<div id="tocRoot"></div>
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<p class="module-desc"><p>This module implements complex numbers and basic mathematical operations on them.</p>
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<p>Complex numbers are currently generic over 64-bit or 32-bit floats.</p>
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|
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<p><strong class="examples_text">Example:</strong></p>
|
|
<pre class="listing"><span class="Keyword">import</span> <span class="Identifier">std</span><span class="Operator">/</span><span class="Identifier">complex</span>
|
|
<span class="Keyword">from</span> <span class="Identifier">std</span><span class="Operator">/</span><span class="Identifier">math</span> <span class="Keyword">import</span> <span class="Identifier">almostEqual</span><span class="Punctuation">,</span> <span class="Identifier">sqrt</span>
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<span class="Keyword">let</span>
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<span class="Identifier">z1</span> <span class="Operator">=</span> <span class="Identifier">complex</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">,</span> <span class="FloatNumber">2.0</span><span class="Punctuation">)</span>
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<span class="Identifier">z2</span> <span class="Operator">=</span> <span class="Identifier">complex</span><span class="Punctuation">(</span><span class="FloatNumber">3.0</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="FloatNumber">4.0</span><span class="Punctuation">)</span>
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<span class="Identifier">assert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">z1</span> <span class="Operator">+</span> <span class="Identifier">z2</span><span class="Punctuation">,</span> <span class="Identifier">complex</span><span class="Punctuation">(</span><span class="FloatNumber">4.0</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="FloatNumber">2.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span>
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<span class="Identifier">assert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">z1</span> <span class="Operator">-</span> <span class="Identifier">z2</span><span class="Punctuation">,</span> <span class="Identifier">complex</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">2.0</span><span class="Punctuation">,</span> <span class="FloatNumber">6.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span>
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<span class="Identifier">assert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">z1</span> <span class="Operator">*</span> <span class="Identifier">z2</span><span class="Punctuation">,</span> <span class="Identifier">complex</span><span class="Punctuation">(</span><span class="FloatNumber">11.0</span><span class="Punctuation">,</span> <span class="FloatNumber">2.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span>
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<span class="Identifier">assert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">z1</span> <span class="Operator">/</span> <span class="Identifier">z2</span><span class="Punctuation">,</span> <span class="Identifier">complex</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">0.2</span><span class="Punctuation">,</span> <span class="FloatNumber">0.4</span><span class="Punctuation">)</span><span class="Punctuation">)</span>
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<span class="Identifier">assert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">abs</span><span class="Punctuation">(</span><span class="Identifier">z1</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="Identifier">sqrt</span><span class="Punctuation">(</span><span class="FloatNumber">5.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span>
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<span class="Identifier">assert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">conjugate</span><span class="Punctuation">(</span><span class="Identifier">z1</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="Identifier">complex</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="FloatNumber">2.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span>
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|
<span class="Keyword">let</span> <span class="Punctuation">(</span><span class="Identifier">r</span><span class="Punctuation">,</span> <span class="Identifier">phi</span><span class="Punctuation">)</span> <span class="Operator">=</span> <span class="Identifier">z1</span><span class="Operator">.</span><span class="Identifier">polar</span>
|
|
<span class="Identifier">assert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">rect</span><span class="Punctuation">(</span><span class="Identifier">r</span><span class="Punctuation">,</span> <span class="Identifier">phi</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="Identifier">z1</span><span class="Punctuation">)</span></pre></p>
|
|
<div class="section" id="6">
|
|
<h1><a class="toc-backref" href="#6">Imports</a></h1>
|
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<dl class="item">
|
|
<a class="reference external" href="math.html">math</a>, <a class="reference external" href="strformat.html">strformat</a>, <a class="reference external" href="strutils.html">strutils</a>
|
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</dl>
|
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</div>
|
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<div class="section" id="7">
|
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<h1><a class="toc-backref" href="#7">Types</a></h1>
|
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<dl class="item">
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<div id="Complex">
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<dt><pre><a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span> <span class="Other">=</span> <span class="Keyword">object</span>
|
|
<span class="Identifier">re</span><span class="Operator">*</span><span class="Other">,</span> <span class="Identifier">im</span><span class="Operator">*</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
|
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<dd>
|
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|
A complex number, consisting of a real and an imaginary part.
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L39" class="link-seesrc" target="_blank">Source</a>
|
|
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L39" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
|
|
<div id="Complex32">
|
|
<dt><pre><a href="complex.html#Complex32"><span class="Identifier">Complex32</span></a> <span class="Other">=</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">]</span></pre></dt>
|
|
<dd>
|
|
|
|
Alias for a complex number using 32-bit floats.
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L44" class="link-seesrc" target="_blank">Source</a>
|
|
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L44" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
|
|
</div>
|
|
<div id="Complex64">
|
|
<dt><pre><a href="complex.html#Complex64"><span class="Identifier">Complex64</span></a> <span class="Other">=</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">]</span></pre></dt>
|
|
<dd>
|
|
|
|
Alias for a complex number using 64-bit floats.
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L42" class="link-seesrc" target="_blank">Source</a>
|
|
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L42" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
|
|
</div>
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|
|
|
</dl>
|
|
</div>
|
|
<div class="section" id="12">
|
|
<h1><a class="toc-backref" href="#12">Procs</a></h1>
|
|
<dl class="item">
|
|
<div id="$-procs-all">
|
|
<div id="$,Complex">
|
|
<dt><pre><span class="Keyword">func</span> <a href="#%24%2CComplex"><span class="Identifier">`$`</span></a><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#string"><span class="Identifier">string</span></a></pre></dt>
|
|
<dd>
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|
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|
Returns <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>'s string representation as <tt class="docutils literal"><span class="pre"><span class="StringLit">"(re, im)"</span></span></tt>.
|
|
<p><strong class="examples_text">Example:</strong></p>
|
|
<pre class="listing"><span class="Identifier">doAssert</span> <span class="Operator">$</span><span class="Identifier">complex</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">,</span> <span class="FloatNumber">2.0</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="StringLit">"(1.0, 2.0)"</span></pre>
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L410" class="link-seesrc" target="_blank">Source</a>
|
|
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L410" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
|
|
<div id="*-procs-all">
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|
<div id="*,Complex[T],Complex[T]">
|
|
<dt><pre><span class="Keyword">func</span> <a href="#%2A%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">`*`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
|
|
<dd>
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|
Multiplies two complex numbers.
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L136" class="link-seesrc" target="_blank">Source</a>
|
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L136" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
|
|
<div id="*,Complex[T],T">
|
|
<dt><pre><span class="Keyword">func</span> <a href="#%2A%2CComplex%5BT%5D%2CT"><span class="Identifier">`*`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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|
Multiplies a complex number with a real number.
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|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L132" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L132" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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<div id="*,T,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#%2A%2CT%2CComplex%5BT%5D"><span class="Identifier">`*`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
|
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<dd>
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|
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|
Multiplies a real number with a complex number.
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L128" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L128" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="*=-procs-all">
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<div id="*=,Complex[T],Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#%2A%3D%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">`*=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
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<dd>
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Multiplies <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> by <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L163" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L163" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="+-procs-all">
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<div id="+,Complex[T],Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#%2B%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">`+`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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|
Adds two complex numbers.
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L108" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L108" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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<div id="+,Complex[T],T">
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|
<dt><pre><span class="Keyword">func</span> <a href="#%2B%2CComplex%5BT%5D%2CT"><span class="Identifier">`+`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Adds a complex number to a real number.
|
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L104" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L104" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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<div id="+,T,Complex[T]">
|
|
<dt><pre><span class="Keyword">func</span> <a href="#%2B%2CT%2CComplex%5BT%5D"><span class="Identifier">`+`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Adds a real number to a complex number.
|
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L100" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L100" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="+=-procs-all">
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<div id="+=,Complex[T],Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#%2B%3D%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">`+=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
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<dd>
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Adds <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> to <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L153" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L153" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="--procs-all">
|
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<div id="-,Complex[T],Complex[T]">
|
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<dt><pre><span class="Keyword">func</span> <a href="#-%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">`-`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Subtracts two complex numbers.
|
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L124" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L124" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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<div id="-,Complex[T],T">
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<dt><pre><span class="Keyword">func</span> <a href="#-%2CComplex%5BT%5D%2CT"><span class="Identifier">`-`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Subtracts a real number from a complex number.
|
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L120" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L120" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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<div id="-,T,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#-%2CT%2CComplex%5BT%5D"><span class="Identifier">`-`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Subtracts a complex number from a real number.
|
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L116" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L116" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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<div id="-,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#-%2CComplex%5BT%5D"><span class="Identifier">`-`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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|
<dd>
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Unary minus for complex numbers.
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|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L112" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L112" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="-=-procs-all">
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<div id="-=,Complex[T],Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#-%3D%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">`-=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
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<dd>
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Subtracts <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> from <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.
|
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L158" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L158" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="/-procs-all">
|
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<div id="/,Complex[T],Complex[T]">
|
|
<dt><pre><span class="Keyword">func</span> <a href="#%2F%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">`/`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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|
<dd>
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Divides two complex numbers.
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L149" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L149" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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<div id="/,Complex[T],T">
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|
<dt><pre><span class="Keyword">func</span> <a href="#%2F%2CComplex%5BT%5D%2CT"><span class="Identifier">`/`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
|
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<dd>
|
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|
Divides a complex number by a real number.
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L141" class="link-seesrc" target="_blank">Source</a>
|
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L141" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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<div id="/,T,Complex[T]">
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|
<dt><pre><span class="Keyword">func</span> <a href="#%2F%2CT%2CComplex%5BT%5D"><span class="Identifier">`/`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
|
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<dd>
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Divides a real number by a complex number.
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L145" class="link-seesrc" target="_blank">Source</a>
|
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L145" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="/=-procs-all">
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<div id="/=,Complex[T],Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#%2F%3D%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">`/=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
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<dd>
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Divides <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> by <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> in place.
|
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L169" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L169" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="==-procs-all">
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<div id="==,Complex[T],Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#%3D%3D%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">`==`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="system.html#bool"><span class="Identifier">bool</span></a></pre></dt>
|
|
<dd>
|
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|
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Compares two complex numbers for equality.
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L96" class="link-seesrc" target="_blank">Source</a>
|
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L96" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="abs-procs-all">
|
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<div id="abs,Complex[T]">
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|
<dt><pre><span class="Keyword">func</span> <a href="#abs%2CComplex%5BT%5D"><span class="Identifier">abs</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
|
|
<dd>
|
|
|
|
Returns the absolute value of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>, that is the distance from (0, 0) to <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L68" class="link-seesrc" target="_blank">Source</a>
|
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L68" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="abs2-procs-all">
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<div id="abs2,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#abs2%2CComplex%5BT%5D"><span class="Identifier">abs2</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
|
|
<dd>
|
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|
Returns the squared absolute value of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>, that is the squared distance from (0, 0) to <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>. This is more efficient than <tt class="docutils literal"><span class="pre"><span class="Identifier">abs</span><span class="Punctuation">(</span><span class="Identifier">z</span><span class="Punctuation">)</span> <span class="Operator">^</span> <span class="DecNumber">2</span></span></tt>.
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L73" class="link-seesrc" target="_blank">Source</a>
|
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L73" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
|
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<div id="almostEqual-procs-all">
|
|
<div id="almostEqual,Complex[T: SomeFloat],Complex[T: SomeFloat],Natural">
|
|
<dt><pre><span class="Keyword">func</span> <a href="#almostEqual%2CComplex%5BT%3A%20SomeFloat%5D%2CComplex%5BT%3A%20SomeFloat%5D%2CNatural"><span class="Identifier">almostEqual</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeFloat"><span class="Identifier">SomeFloat</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">unitsInLastPlace</span><span class="Other">:</span> <a href="system.html#Natural"><span class="Identifier">Natural</span></a> <span class="Other">=</span> <span class="DecNumber">4</span><span class="Other">)</span><span class="Other">:</span> <a href="system.html#bool"><span class="Identifier">bool</span></a></pre></dt>
|
|
<dd>
|
|
|
|
<p>Checks if two complex values are almost equal, using the <a class="reference external" href="https://en.wikipedia.org/wiki/Machine_epsilon">machine epsilon</a>.</p>
|
|
<p>Two complex values are considered almost equal if their real and imaginary components are almost equal.</p>
|
|
<p><tt class="docutils literal"><span class="pre"><span class="Identifier">unitsInLastPlace</span></span></tt> is the max number of <a class="reference external" href="https://en.wikipedia.org/wiki/Unit_in_the_last_place">units in the last place</a> difference tolerated when comparing two numbers. The larger the value, the more error is allowed. A <tt class="docutils literal"><span class="pre"><span class="DecNumber">0</span></span></tt> value means that two numbers must be exactly the same to be considered equal.</p>
|
|
<p>The machine epsilon has to be scaled to the magnitude of the values used and multiplied by the desired precision in ULPs unless the difference is subnormal.</p>
|
|
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L391" class="link-seesrc" target="_blank">Source</a>
|
|
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L391" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
|
|
</div>
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</div>
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<div id="arccos-procs-all">
|
|
<div id="arccos,Complex[T]">
|
|
<dt><pre><span class="Keyword">func</span> <a href="#arccos%2CComplex%5BT%5D"><span class="Identifier">arccos</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the inverse cosine of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L281" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L281" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="arccosh-procs-all">
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<div id="arccosh,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#arccosh%2CComplex%5BT%5D"><span class="Identifier">arccosh</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the inverse hyperbolic cosine of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L329" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L329" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="arccot-procs-all">
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<div id="arccot,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#arccot%2CComplex%5BT%5D"><span class="Identifier">arccot</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the inverse cotangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L297" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L297" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="arccoth-procs-all">
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<div id="arccoth,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#arccoth%2CComplex%5BT%5D"><span class="Identifier">arccoth</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the inverse hyperbolic cotangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L345" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L345" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="arccsc-procs-all">
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<div id="arccsc,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#arccsc%2CComplex%5BT%5D"><span class="Identifier">arccsc</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the inverse cosecant of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L313" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L313" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="arccsch-procs-all">
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<div id="arccsch,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#arccsch%2CComplex%5BT%5D"><span class="Identifier">arccsch</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the inverse hyperbolic cosecant of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L361" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L361" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="arcsec-procs-all">
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<div id="arcsec,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#arcsec%2CComplex%5BT%5D"><span class="Identifier">arcsec</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the inverse secant of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L305" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L305" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="arcsech-procs-all">
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<div id="arcsech,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#arcsech%2CComplex%5BT%5D"><span class="Identifier">arcsech</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the inverse hyperbolic secant of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L353" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L353" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="arcsin-procs-all">
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<div id="arcsin,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#arcsin%2CComplex%5BT%5D"><span class="Identifier">arcsin</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the inverse sine of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L271" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L271" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="arcsinh-procs-all">
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<div id="arcsinh,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#arcsinh%2CComplex%5BT%5D"><span class="Identifier">arcsinh</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the inverse hyperbolic sine of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L321" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L321" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="arctan-procs-all">
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<div id="arctan,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#arctan%2CComplex%5BT%5D"><span class="Identifier">arctan</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the inverse tangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
|
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L289" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L289" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="arctanh-procs-all">
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<div id="arctanh,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#arctanh%2CComplex%5BT%5D"><span class="Identifier">arctanh</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the inverse hyperbolic tangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L337" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L337" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="complex-procs-all">
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<div id="complex,T,T">
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<dt><pre><span class="Keyword">func</span> <a href="#complex%2CT%2CT"><span class="Identifier">complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeFloat"><span class="Identifier">SomeFloat</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">re</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">im</span><span class="Other">:</span> <span class="Identifier">T</span> <span class="Other">=</span> <span class="FloatNumber">0.0</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns a <tt class="docutils literal"><span class="pre"><span class="Identifier">Complex</span><span class="Punctuation">[</span><span class="Identifier">T</span><span class="Punctuation">]</span></span></tt> with real part <tt class="docutils literal"><span class="pre"><span class="Identifier">re</span></span></tt> and imaginary part <tt class="docutils literal"><span class="pre"><span class="Identifier">im</span></span></tt>.
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L47" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L47" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="complex32-procs-all">
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<div id="complex32,float32,float32">
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<dt><pre><span class="Keyword">func</span> <a href="#complex32%2Cfloat32%2Cfloat32"><span class="Identifier">complex32</span></a><span class="Other">(</span><span class="Identifier">re</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">;</span> <span class="Identifier">im</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Other">=</span> <span class="FloatNumber">0.0</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex32"><span class="Identifier">Complex32</span></a> {.<span><span class="Other pragmadots">...</span></span><span class="pragmawrap"><span class="Identifier">raises</span><span class="Other">:</span> <span class="Other">[</span><span class="Other">]</span><span class="Other">,</span>
|
|
<span class="Identifier">tags</span><span class="Other">:</span> <span class="Other">[</span><span class="Other">]</span><span class="Other">,</span> <span class="Identifier">forbids</span><span class="Other">:</span> <span class="Other">[</span><span class="Other">]</span></span>.}</pre></dt>
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<dd>
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Returns a <tt class="docutils literal"><span class="pre"><span class="Identifier">Complex32</span></span></tt> with real part <tt class="docutils literal"><span class="pre"><span class="Identifier">re</span></span></tt> and imaginary part <tt class="docutils literal"><span class="pre"><span class="Identifier">im</span></span></tt>.
|
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L51" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L51" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="complex64-procs-all">
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<div id="complex64,float64,float64">
|
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<dt><pre><span class="Keyword">func</span> <a href="#complex64%2Cfloat64%2Cfloat64"><span class="Identifier">complex64</span></a><span class="Other">(</span><span class="Identifier">re</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">;</span> <span class="Identifier">im</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> <span class="Other">=</span> <span class="FloatNumber">0.0</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex64"><span class="Identifier">Complex64</span></a> {.<span><span class="Other pragmadots">...</span></span><span class="pragmawrap"><span class="Identifier">raises</span><span class="Other">:</span> <span class="Other">[</span><span class="Other">]</span><span class="Other">,</span>
|
|
<span class="Identifier">tags</span><span class="Other">:</span> <span class="Other">[</span><span class="Other">]</span><span class="Other">,</span> <span class="Identifier">forbids</span><span class="Other">:</span> <span class="Other">[</span><span class="Other">]</span></span>.}</pre></dt>
|
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<dd>
|
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|
Returns a <tt class="docutils literal"><span class="pre"><span class="Identifier">Complex64</span></span></tt> with real part <tt class="docutils literal"><span class="pre"><span class="Identifier">re</span></span></tt> and imaginary part <tt class="docutils literal"><span class="pre"><span class="Identifier">im</span></span></tt>.
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L55" class="link-seesrc" target="_blank">Source</a>
|
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L55" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="conjugate-procs-all">
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<div id="conjugate,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#conjugate%2CComplex%5BT%5D"><span class="Identifier">conjugate</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the complex conjugate of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt> (<tt class="docutils literal"><span class="pre"><span class="Identifier">complex</span><span class="Punctuation">(</span><span class="Identifier">z</span><span class="Operator">.</span><span class="Identifier">re</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="Identifier">z</span><span class="Operator">.</span><span class="Identifier">im</span><span class="Punctuation">)</span></span></tt>).
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L88" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L88" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="cos-procs-all">
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<div id="cos,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#cos%2CComplex%5BT%5D"><span class="Identifier">cos</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the cosine of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L275" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L275" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="cosh-procs-all">
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<div id="cosh,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#cosh%2CComplex%5BT%5D"><span class="Identifier">cosh</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the hyperbolic cosine of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L325" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L325" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="cot-procs-all">
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<div id="cot,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#cot%2CComplex%5BT%5D"><span class="Identifier">cot</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the cotangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L293" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L293" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="coth-procs-all">
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<div id="coth,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#coth%2CComplex%5BT%5D"><span class="Identifier">coth</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the hyperbolic cotangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L341" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L341" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="csc-procs-all">
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<div id="csc,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#csc%2CComplex%5BT%5D"><span class="Identifier">csc</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the cosecant of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L309" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L309" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="csch-procs-all">
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<div id="csch,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#csch%2CComplex%5BT%5D"><span class="Identifier">csch</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the hyperbolic cosecant of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L357" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L357" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="exp-procs-all">
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<div id="exp,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#exp%2CComplex%5BT%5D"><span class="Identifier">exp</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Computes the exponential function (<tt class="docutils literal"><span class="pre"><span class="Identifier">e</span><span class="Operator">^</span><span class="Identifier">z</span></span></tt>).
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L198" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L198" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="formatValue-procs-all">
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<div id="formatValue,string,Complex,string">
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<dt><pre><span class="Keyword">proc</span> <a href="#formatValue%2Cstring%2CComplex%2Cstring"><span class="Identifier">formatValue</span></a><span class="Other">(</span><span class="Identifier">result</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="system.html#string"><span class="Identifier">string</span></a><span class="Other">;</span> <span class="Identifier">value</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">;</span> <span class="Identifier">specifier</span><span class="Other">:</span> <a href="system.html#string"><span class="Identifier">string</span></a><span class="Other">)</span></pre></dt>
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<dd>
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Standard format implementation for <tt class="docutils literal"><span class="pre"><span class="Identifier">Complex</span></span></tt>. It makes little sense to call this directly, but it is required to exist by the <tt class="docutils literal"><span class="pre"><span class="Operator">&</span></span></tt> macro. For complex numbers, we add a specific 'j' specifier, which formats the value as (A+Bj) like in mathematics.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L439" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L439" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="inv-procs-all">
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<div id="inv,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#inv%2CComplex%5BT%5D"><span class="Identifier">inv</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the multiplicative inverse of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt> (<tt class="docutils literal"><span class="pre"><span class="DecNumber">1</span><span class="Operator">/</span><span class="Identifier">z</span></span></tt>).
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L92" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L92" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="ln-procs-all">
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<div id="ln,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#ln%2CComplex%5BT%5D"><span class="Identifier">ln</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the (<a class="reference external" href="https://en.wikipedia.org/wiki/Complex_logarithm#Principal_value">principal value</a> of the) natural logarithm of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L205" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L205" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="log2-procs-all">
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<div id="log2,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#log2%2CComplex%5BT%5D"><span class="Identifier">log2</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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<p>Returns the logarithm base 2 of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.</p>
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<p><strong>See also:</strong></p>
|
|
<ul class="simple"><li><a class="reference external" href="#ln,Complex[T]">ln func</a></li>
|
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</ul>
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L218" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L218" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="log10-procs-all">
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<div id="log10,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#log10%2CComplex%5BT%5D"><span class="Identifier">log10</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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<p>Returns the logarithm base 10 of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.</p>
|
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<p><strong>See also:</strong></p>
|
|
<ul class="simple"><li><a class="reference external" href="#ln,Complex[T]">ln func</a></li>
|
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</ul>
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L211" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L211" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="phase-procs-all">
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<div id="phase,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#phase%2CComplex%5BT%5D"><span class="Identifier">phase</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
|
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<dd>
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Returns the phase (or argument) of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>, that is the angle in polar representation.<p><tt class="docutils literal"><span class="pre"><span class="Identifier">result</span> <span class="Operator">=</span> <span class="Identifier">arctan2</span><span class="Punctuation">(</span><span class="Identifier">z</span><span class="Operator">.</span><span class="Identifier">im</span><span class="Punctuation">,</span> <span class="Identifier">z</span><span class="Operator">.</span><span class="Identifier">re</span><span class="Punctuation">)</span></span></tt><br/></p>
|
|
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L365" class="link-seesrc" target="_blank">Source</a>
|
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L365" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="polar-procs-all">
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<div id="polar,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#polar%2CComplex%5BT%5D"><span class="Identifier">polar</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <span class="Keyword">tuple</span><span class="Other">[</span><span class="Identifier">r</span><span class="Other">,</span> <span class="Identifier">phi</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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|
Returns <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt> in polar coordinates.<p><tt class="docutils literal"><span class="pre"><span class="Identifier">result</span><span class="Operator">.</span><span class="Identifier">r</span> <span class="Operator">=</span> <span class="Identifier">abs</span><span class="Punctuation">(</span><span class="Identifier">z</span><span class="Punctuation">)</span></span></tt><br/><tt class="docutils literal"><span class="pre"><span class="Identifier">result</span><span class="Operator">.</span><span class="Identifier">phi</span> <span class="Operator">=</span> <span class="Identifier">phase</span><span class="Punctuation">(</span><span class="Identifier">z</span><span class="Punctuation">)</span></span></tt><br/></p><p><strong>See also:</strong></p>
|
|
<ul class="simple"><li><a class="reference external" href="#rect,T,T">rect func</a> for the inverse operation</li>
|
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</ul>
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L371" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L371" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="pow-procs-all">
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<div id="pow,Complex[T],Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#pow%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">pow</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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<tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> raised to the power of <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
|
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L225" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L225" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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<div id="pow,Complex[T],T">
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<dt><pre><span class="Keyword">func</span> <a href="#pow%2CComplex%5BT%5D%2CT"><span class="Identifier">pow</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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The complex number <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> raised to the power of the real number <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L263" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L263" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="rect-procs-all">
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<div id="rect,T,T">
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<dt><pre><span class="Keyword">func</span> <a href="#rect%2CT%2CT"><span class="Identifier">rect</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">r</span><span class="Other">,</span> <span class="Identifier">phi</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the complex number with polar coordinates <tt class="docutils literal"><span class="pre"><span class="Identifier">r</span></span></tt> and <tt class="docutils literal"><span class="pre"><span class="Identifier">phi</span></span></tt>.<p><tt class="docutils literal"><span class="pre"><span class="Identifier">result</span><span class="Operator">.</span><span class="Identifier">re</span> <span class="Operator">=</span> <span class="Identifier">r</span> <span class="Operator">*</span> <span class="Identifier">cos</span><span class="Punctuation">(</span><span class="Identifier">phi</span><span class="Punctuation">)</span></span></tt><br/><tt class="docutils literal"><span class="pre"><span class="Identifier">result</span><span class="Operator">.</span><span class="Identifier">im</span> <span class="Operator">=</span> <span class="Identifier">r</span> <span class="Operator">*</span> <span class="Identifier">sin</span><span class="Punctuation">(</span><span class="Identifier">phi</span><span class="Punctuation">)</span></span></tt><br/></p><p><strong>See also:</strong></p>
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<ul class="simple"><li><a class="reference external" href="#polar,Complex[T]">polar func</a> for the inverse operation</li>
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</ul>
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L381" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L381" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="sec-procs-all">
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<div id="sec,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#sec%2CComplex%5BT%5D"><span class="Identifier">sec</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the secant of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L301" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L301" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="sech-procs-all">
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<div id="sech,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#sech%2CComplex%5BT%5D"><span class="Identifier">sech</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the hyperbolic secant of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L349" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L349" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="sgn-procs-all">
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<div id="sgn,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#sgn%2CComplex%5BT%5D"><span class="Identifier">sgn</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the phase of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt> as a unit complex number, or 0 if <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt> is 0.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L79" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L79" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="sin-procs-all">
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<div id="sin,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#sin%2CComplex%5BT%5D"><span class="Identifier">sin</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the sine of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L267" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L267" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="sinh-procs-all">
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<div id="sinh,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#sinh%2CComplex%5BT%5D"><span class="Identifier">sinh</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the hyperbolic sine of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L317" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L317" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="sqrt-procs-all">
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<div id="sqrt,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#sqrt%2CComplex%5BT%5D"><span class="Identifier">sqrt</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Computes the (<a class="reference external" href="https://en.wikipedia.org/wiki/Square_root#Principal_square_root_of_a_complex_number">principal</a>) square root of a complex number <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L174" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L174" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="tan-procs-all">
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<div id="tan,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#tan%2CComplex%5BT%5D"><span class="Identifier">tan</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the tangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L285" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L285" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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<div id="tanh-procs-all">
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<div id="tanh,Complex[T]">
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<dt><pre><span class="Keyword">func</span> <a href="#tanh%2CComplex%5BT%5D"><span class="Identifier">tanh</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
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<dd>
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Returns the hyperbolic tangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L333" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L333" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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</dl>
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</div>
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<div class="section" id="18">
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<h1><a class="toc-backref" href="#18">Templates</a></h1>
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<dl class="item">
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<div id="im-templates-all">
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<div id="im.t,float32">
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<dt><pre><span class="Keyword">template</span> <a href="#im.t%2Cfloat32"><span class="Identifier">im</span></a><span class="Other">(</span><span class="Identifier">arg</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex32"><span class="Identifier">Complex32</span></a></pre></dt>
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<dd>
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Returns <tt class="docutils literal"><span class="pre"><span class="Identifier">arg</span></span></tt> as an imaginary number (<tt class="docutils literal"><span class="pre"><span class="Identifier">complex32</span><span class="Punctuation">(</span><span class="DecNumber">0</span><span class="Punctuation">,</span> <span class="Identifier">arg</span><span class="Punctuation">)</span></span></tt>).
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L63" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L63" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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<div id="im.t,float64">
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<dt><pre><span class="Keyword">template</span> <a href="#im.t%2Cfloat64"><span class="Identifier">im</span></a><span class="Other">(</span><span class="Identifier">arg</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex64"><span class="Identifier">Complex64</span></a></pre></dt>
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<dd>
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Returns <tt class="docutils literal"><span class="pre"><span class="Identifier">arg</span></span></tt> as an imaginary number (<tt class="docutils literal"><span class="pre"><span class="Identifier">complex64</span><span class="Punctuation">(</span><span class="DecNumber">0</span><span class="Punctuation">,</span> <span class="Identifier">arg</span><span class="Punctuation">)</span></span></tt>).
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L65" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L65" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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<div id="im.t,typedesc[float32]">
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<dt><pre><span class="Keyword">template</span> <a href="#im.t%2Ctypedesc%5Bfloat32%5D"><span class="Identifier">im</span></a><span class="Other">(</span><span class="Identifier">arg</span><span class="Other">:</span> <a href="system.html#typedesc"><span class="Identifier">typedesc</span></a><span class="Other">[</span><a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex32"><span class="Identifier">Complex32</span></a></pre></dt>
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<dd>
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Returns the imaginary unit (<tt class="docutils literal"><span class="pre"><span class="Identifier">complex32</span><span class="Punctuation">(</span><span class="DecNumber">0</span><span class="Punctuation">,</span> <span class="DecNumber">1</span><span class="Punctuation">)</span></span></tt>).
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L59" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L59" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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<div id="im.t,typedesc[float64]">
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<dt><pre><span class="Keyword">template</span> <a href="#im.t%2Ctypedesc%5Bfloat64%5D"><span class="Identifier">im</span></a><span class="Other">(</span><span class="Identifier">arg</span><span class="Other">:</span> <a href="system.html#typedesc"><span class="Identifier">typedesc</span></a><span class="Other">[</span><a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex64"><span class="Identifier">Complex64</span></a></pre></dt>
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<dd>
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Returns the imaginary unit (<tt class="docutils literal"><span class="pre"><span class="Identifier">complex64</span><span class="Punctuation">(</span><span class="DecNumber">0</span><span class="Punctuation">,</span> <span class="DecNumber">1</span><span class="Punctuation">)</span></span></tt>).
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<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L61" class="link-seesrc" target="_blank">Source</a>
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<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L61" class="link-seesrc" target="_blank" >Edit</a>
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</dd>
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</div>
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</div>
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</dl>
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</div>
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<small style="color: var(--hint);">Made with Nim. Generated: 2025-12-28 15:55:01 UTC</small>
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