/// <summary>
/// Raise this <c>Complex</c> to the given value.
/// </summary>
/// <param name="complex">The <see cref="Complex"/> number to perfom this operation on.</param>
/// <param name="exponent">
/// The exponent.
/// </param>
/// <returns>
/// The complex number raised to the given exponent.
/// </returns>
public static Complex Power(this Complex complex, Complex exponent)
{
if (complex.IsZero())
{
if (exponent.IsZero())
{
return(Complex.One);
}
if (exponent.Real > 0d)
{
return(Complex.Zero);
}
if (exponent.Real < 0d)
{
return(exponent.Imaginary == 0d
? new Complex(double.PositiveInfinity, 0d)
: new Complex(double.PositiveInfinity, double.PositiveInfinity));
}
return(new Complex(double.NaN, double.NaN));
}
return(Complex.Pow(complex, exponent));
}
/// <summary>
/// Raise this <c>Complex</c> to the given value.
/// </summary>
/// <param name="complex">The <see cref="Complex"/> number to perfom this operation on.</param>
/// <param name="exponent">
/// The exponent.
/// </param>
/// <returns>
/// The complex number raised to the given exponent.
/// </returns>
public static Complex Power(this Complex complex, Complex exponent)
{
if (complex.IsZero())
{
if (exponent.IsZero())
{
return(Complex.One);
}
if (exponent.Real > 0.0)
{
return(Complex.Zero);
}
if (exponent.Real < 0)
{
if (exponent.Imaginary == 0.0)
{
return(new Complex(double.PositiveInfinity, 0.0));
}
return(new Complex(double.PositiveInfinity, double.PositiveInfinity));
}
return(double.NaN);
}
return((exponent * complex.NaturalLogarithm()).Exponential());
}
/// <summary>
/// Trigonometric Arc Cotangent of this <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The arc cotangent of a complex number.
/// </returns>
public static Complex InverseCotangent(this Complex value)
{
if (value.IsZero())
{
return(Math.PI / 2.0);
}
var inv = Complex.ImaginaryOne / value;
return((Complex.ImaginaryOne * 0.5) * ((1.0 - inv).NaturalLogarithm() - (1.0 + inv).NaturalLogarithm()));
}
/// <summary>
/// Trigonometric principal Arc Cotangent of this <c>Complex</c> number.
/// </summary>
/// <param name="value">The complex value.</param>
/// <returns>The arc cotangent of a complex number.</returns>
public static Complex Acot(this Complex value)
{
if (value.IsZero())
{
return(Constants.PiOver2);
}
var inv = Complex.ImaginaryOne / value;
return((Complex.ImaginaryOne * 0.5) * ((1.0 - inv).Ln() - (1.0 + inv).Ln()));
}
