diff --git a/lib/pure/complex.nim b/lib/pure/complex.nim index dc899a2f76..8234db410b 100644 --- a/lib/pure/complex.nim +++ b/lib/pure/complex.nim @@ -249,14 +249,31 @@ func pow*[T](x, y: Complex[T]): Complex[T] = else: result.re = 0.0 result.im = 0.0 - elif y.re == 1.0 and y.im == 0.0: - result = x - elif y.re == -1.0 and y.im == 0.0: - result = T(1.0) / x - elif y.re == 2.0 and y.im == 0.0: - result = x * x - elif y.re == 0.5 and y.im == 0.0: - result = sqrt(x) + elif y.im == 0.0: + if y.re == 1.0: + result = x + elif y.re == -1.0: + result = T(1.0) / x + elif y.re == 2.0: + result = x * x + elif y.re == 0.5: + result = sqrt(x) + elif x.im == 0.0: + # Revert to real pow when both base and exponent are real + result.re = pow(x.re, y.re) + result.im = 0.0 + else: + # Special case when the exponent is real + let + rho = abs(x) + theta = arctan2(x.im, x.re) + s = pow(rho, y.re) + r = y.re * theta + result.re = s * cos(r) + result.im = s * sin(r) + elif x.im == 0.0 and x.re == E: + # Special case Euler's formula + result = exp(y) else: let rho = abs(x)