/// <summary>
/// Evaluate all cubic roots of this <c>Complex</c>.
/// </summary>
public static (Complex, Complex, Complex) CubicRoots(this Complex complex)
{
var r = Math.Pow(complex.Magnitude, 1d / 3d);
var theta = complex.Phase / 3;
const double shift = Constants.Pi2 / 3;
return(Complex.FromPolarCoordinates(r, theta),
Complex.FromPolarCoordinates(r, theta + shift),
Complex.FromPolarCoordinates(r, theta - shift));
}
/// <summary>
/// Evaluate all cubic roots of this <c>Complex</c>.
/// Modified from https://github.com/mathnet/mathnet-numerics/blob/master/src/Numerics/ComplexExtensions.cs
/// </summary>
public static (Complex, Complex, Complex) ComplexCubeRoot(Complex complex)
{
double r = Math.Pow(complex.Magnitude, 1.0 / 3.0);
double theta = complex.Phase / 3.0;
const double shift = Math.PI * 2.0 / 3.0;
return(Complex.FromPolarCoordinates(r, theta),
Complex.FromPolarCoordinates(r, theta + shift),
Complex.FromPolarCoordinates(r, theta - shift));
}
