/// <summary>
/// Trigonometric principal Arc Cosine of this <c>Complex</c> number.
/// </summary>
/// <param name="value">The complex value.</param>
/// <returns>The arc cosine of a complex number.</returns>
public static Complex Acos(this Complex value)
{
if (value.Imaginary < 0 || value.Imaginary == 0d && value.Real > 0)
{
return(Constants.Pi - Acos(-value));
}
return(-Complex.ImaginaryOne * (value + (Complex.ImaginaryOne * (1 - value.Square()).SquareRoot())).Ln());
}
/// <summary>
/// Trigonometric principal Arc Sine of this <c>Complex</c> number.
/// </summary>
/// <param name="value">The complex value.</param>
/// <returns>The arc sine of a complex number.</returns>
public static Complex Asin(this Complex value)
{
if (value.Imaginary > 0 || value.Imaginary == 0d && value.Real < 0)
{
return(-Asin(-value));
}
return(-Complex.ImaginaryOne * ((1 - value.Square()).SquareRoot() + (Complex.ImaginaryOne * value)).Ln());
}
/// <summary>Trigonometric Hyperbolic Cosecant (Cosecans hyperbolicus) of this <c>Complex</c>.</summary>
public Complex Csch()
{
if (IsReal)
{
return(new Complex(Trig.Csch(real), 0d));
}
Complex exp = this.Exp();
return(2 * exp / (exp.Square() - 1));
}
/// <summary>
/// Trigonometric Arc Sine of this <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The arc sine of a complex number.
/// </returns>
public static Complex InverseSine(this Complex value)
{
return(-Complex.ImaginaryOne * ((1 - value.Square()).SquareRoot() + (Complex.ImaginaryOne * value)).NaturalLogarithm());
}
/// <summary>
/// Trigonometric Hyperbolic Arc Sine of this <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The hyperbolic arc sine of a complex number.
/// </returns>
public static Complex InverseHyperbolicSine(this Complex value)
{
return((value + (value.Square() + 1).SquareRoot()).NaturalLogarithm());
}
/// <summary>Trigonometric Hyperbolic Area Cosecant (Areacosekans hyperbolicus) of this <c>Complex</c>.</summary>
public Complex Acsch()
{
Complex inv = 1 / this;
return((inv + (inv.Square() + 1).Sqrt()).Ln());
}
/// <summary>Trigonometric Arcus Cosecant (Arkuscosekans) of this <c>Complex</c>.</summary>
public Complex Acsc()
{
Complex inv = 1 / this;
return(-Complex.I * (Complex.I * inv + (1 - inv.Square()).Sqrt()).Ln());
}
/// <summary>Trigonometric Arcus Secant (Arkussekans) of this <c>Complex</c>.</summary>
public Complex Asec()
{
Complex inv = 1 / this;
return(-Complex.I * (inv + Complex.I * (1 - inv.Square()).Sqrt()).Ln());
}
/// <summary>
/// Hyperbolic Area Sine of this <c>Complex</c> number.
/// </summary>
/// <param name="value">The complex value.</param>
/// <returns>The hyperbolic arc sine of a complex number.</returns>
public static Complex Asinh(this Complex value)
{
return((value + (value.Square() + 1).SquareRoot()).Ln());
}
