/// <summary>
/// Calculates both Square-Roots of a complex number
/// </summary>
/// <param name="number"></param>
/// <returns></returns>
public ComplexD[] Sqrt(ComplexD number)
{
ComplexD res0 = ComplexD.CreateRadial((double)System.Math.Sqrt(number.Norm), number.Argument / 2.0f);
ComplexD res1 = ComplexD.CreateRadial((double)System.Math.Sqrt(number.Norm), number.Argument / 2.0f + (double)Constant.Pi);
return new ComplexD[2] { res0, res1 };
}
/// <summary>
/// Exponentiates a complex by another
/// </summary>
/// <returns></returns>
public static ComplexD Pow(ComplexD number, ComplexD exponent)
{
double r = number.Norm;
double phi = number.Argument;
double a = exponent.Real;
double b = exponent.Imag;
return ComplexD.CreateRadial((double)System.Math.Exp(System.Math.Log(r) * a - b * phi), a * phi + b * (double)System.Math.Log(r));
}
/// <summary>
/// Calculates the n-th Root of a Complex number and returns n Solutions
/// </summary>
/// <param name="number"></param>
/// <param name="order">n</param>
/// <returns></returns>
public ComplexD[] Root(ComplexD number, int order)
{
ComplexD[] values = new ComplexD[order];
double phi = number.Argument / 2.0f;
double dphi = (double)Constant.PiTimesTwo / (double)order;
double r = (double)System.Math.Pow(number.Norm, 1.0f / order);
for (int i = 1; i < order; i++)
{
values[i] = ComplexD.CreateRadial(r, phi + dphi * i);
}
return values;
}
