/// <summary>
/// e. g. Log(2, 32) = 5
/// </summary>
/// <param name="base">
/// Log's base, log(base, x) is a number y such that base^y = x
/// </param>
/// <param name="x">
/// The number of which we want to get its base power
/// </param>
/// <returns></returns>
public static ComplexNumber Log(RealNumber @base, Number x)
{
var baseCom = @base.AsComplexNumber();
var poweredCom = x.AsComplexNumber();
if (baseCom.IsDefinite() && poweredCom.IsDefinite())
{
return(Functional.Downcast(
Complex.Log(x.AsComplex(), @base.AsDouble())
) as ComplexNumber);
}
else
{
return(ComplexNumber.Indefinite(RealNumber.UndefinedState.NAN));
}
}
/// <summary>
/// Calculates the exact value of arccotangent of num
/// </summary>
/// <param name="num"></param>
/// <returns></returns>
public static ComplexNumber Arccotan(Number num)
=> (num as ComplexNumber).IsDefinite()
? Functional.Downcast(Complex.Atan(1 / num.AsComplex())) as ComplexNumber
: RealNumber.NaN();
/// <summary>
/// Calculates the exact value of cosine of num
/// </summary>
/// <param name="num"></param>
/// <returns></returns>
public static ComplexNumber Cos(Number num)
=> (num as ComplexNumber).IsDefinite()
? Functional.Downcast(Complex.Cos(num.AsComplex())) as ComplexNumber
: RealNumber.NaN();