public static ComplexNumber Reciprocal(ComplexNumber c)
{
if (c.IsReal())
{
return(new ComplexNumber(1.0 / c.Real));
}
else
{
double square = Square(c);
return(new ComplexNumber(c.Real / square, -c.Img / square));
}
}
public static ComplexNumber Exp(ComplexNumber exponent)
{
if (exponent.IsReal())
{
return(Math.Exp(exponent.Real));
}
double newRadius = Math.Exp(exponent.Real);
double newAngle = exponent.Img;
return(ComplexNumber.FromPolarCoordinates(newRadius, newAngle));
}
public static ComplexNumber Pow(ComplexNumber theBase, ComplexNumber exponent)
{
if (exponent.IsReal())
{
return(Pow(theBase, exponent.Real));
}
double baseRadius = theBase.PolarRadius;
double baseAngle = theBase.PolarAngleInRadians;
double newRadius = Math.Pow(baseRadius, exponent.Real) * Math.Exp(-baseAngle * exponent.Img);
double newAngle = exponent.Img * Math.Log(baseRadius) + exponent.Real * baseAngle;
return(ComplexNumber.FromPolarCoordinates(newRadius, newAngle));
}
// same funtionality as below, but more efficient if we know exponent isn't complex
public static ComplexNumber Pow(ComplexNumber theBase, double exponent)
{
if (theBase.Real >= 0 && theBase.IsReal())
{
return(Math.Pow(theBase.Real, exponent));
}
double baseRadius = theBase.PolarRadius;
double baseAngle = theBase.PolarAngleInRadians;
double newRadius = Math.Pow(baseRadius, exponent);
double newAngle = exponent * baseAngle;
return(ComplexNumber.FromPolarCoordinates(newRadius, newAngle));
}