/// <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 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)
{
if (value.Imaginary > 0 || value.Imaginary == 0d && value.Real < 0)
{
return(-InverseSine(-value));
}
return(-Complex.ImaginaryOne * ((1 - value.Square()).SquareRoot() + (Complex.ImaginaryOne * value)).NaturalLogarithm());
}
/// <summary>
/// Trigonometric 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 InverseCosine(this Complex value)
{
if (value.Imaginary < 0 || value.Imaginary == 0d && value.Real > 0)
{
return(Constants.Pi - InverseCosine(-value));
}
return(-Complex.ImaginaryOne * (value + (Complex.ImaginaryOne * (1 - value.Square()).SquareRoot())).NaturalLogarithm());
}
public void CanComputeSquare()
{
var complex = new Complex(1.19209289550780998537e-7, 1.19209289550780998537e-7);
AssertHelpers.AlmostEqualRelative(new Complex(0, 2.8421709430403888e-14), complex.Square(), 15);
complex = new Complex(0.0, 1.19209289550780998537e-7);
AssertHelpers.AlmostEqualRelative(new Complex(-1.4210854715201944e-14, 0.0), complex.Square(), 15);
complex = new Complex(0.0, -1.19209289550780998537e-7);
AssertHelpers.AlmostEqualRelative(new Complex(-1.4210854715201944e-14, 0.0), complex.Square(), 15);
complex = new Complex(0.0, 0.5);
AssertHelpers.AlmostEqualRelative(new Complex(-0.25, 0.0), complex.Square(), 15);
complex = new Complex(0.0, -0.5);
AssertHelpers.AlmostEqualRelative(new Complex(-0.25, 0.0), complex.Square(), 15);
complex = new Complex(0.0, -8.388608e6);
AssertHelpers.AlmostEqualRelative(new Complex(-70368744177664.0, 0.0), complex.Square(), 15);
}
/// <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());
}
/// <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());
}
