/// <summary>Trigonometric Hyperbolic Cosine (cosh, Cosinus hyperbolicus) of this <c>Complex</c>.</summary>
public Complex HyperbolicCosine()
{
if (IsReal)
{
return(new Complex(Trig.HyperbolicCosine(real), 0d));
}
return(new Complex(Trig.HyperbolicCosine(real) * Trig.Cosine(imag), Trig.HyperbolicSine(real) * Trig.Sine(imag)));
}
/// <summary>Exponential of this <c>Complex</c> (exp(x), E^x).</summary>
public Complex Exponential()
{
double exp = Math.Exp(real);
if (IsReal)
{
return(new Complex(exp, 0d));
}
return(new Complex(exp * Trig.Cosine(imag), exp * Trig.Sine(imag)));
}
/// <summary>
/// Exponential of this <c>Complex</c> (exp(x), E^x).
/// </summary>
/// <param name="complex">The <see cref="Complex"/> number to perfom this operation on.</param>
/// <returns>
/// The exponential of this complex number.
/// </returns>
public static Complex Exponential(this Complex complex)
{
var exp = Math.Exp(complex.Real);
if (complex.IsReal())
{
return(new Complex(exp, 0.0));
}
return(new Complex(exp * Trig.Cosine(complex.Imaginary), exp * Trig.Sine(complex.Imaginary)));
}
/// <summary>Trigonometric Hyperbolic Cotangent (coth, Cotangens hyperbolicus) of this <c>Complex</c>.</summary>
public Complex HyperbolicCotangent()
{
if (IsReal)
{
return(new Complex(Trig.HyperbolicCotangent(real), 0d));
}
double sini = Trig.Sine(imag);
double sinhr = Trig.HyperbolicSine(real);
double denom = sini * sini + sinhr * sinhr;
return(new Complex(sinhr * Trig.HyperbolicCosine(real) / denom, sini * Trig.Cosine(imag) / denom));
}
/// <summary>Trigonometric Hyperbolic Tangent (tanh, Tangens hyperbolicus) of this <c>Complex</c>.</summary>
public Complex HyperbolicTangent()
{
if (IsReal)
{
return(new Complex(Trig.HyperbolicTangent(real), 0d));
}
double cosi = Trig.Cosine(imag);
double sinhr = Trig.HyperbolicSine(real);
double denom = cosi * cosi + sinhr * sinhr;
return(new Complex(Trig.HyperbolicCosine(real) * sinhr / denom, cosi * Trig.Sine(imag) / denom));
}
/// <summary>Trigonometric Cosecant (csc, Cosekans) of this <c>Complex</c>.</summary>
public Complex Cosecant()
{
if (IsReal)
{
return(new Complex(Trig.Cosecant(real), 0d));
}
double sinr = Trig.Sine(real);
double sinhi = Trig.HyperbolicSine(imag);
double denom = sinr * sinr + sinhi * sinhi;
return(new Complex(sinr * Trig.HyperbolicCosine(imag) / denom, -Trig.Cosine(real) * sinhi / denom));
}
/// <summary>Trigonometric Secant (sec, Sekans) of this <c>Complex</c>.</summary>
public Complex Secant()
{
if (IsReal)
{
return(new Complex(Trig.Secant(real), 0d));
}
double cosr = Trig.Cosine(real);
double sinhi = Trig.HyperbolicSine(imag);
double denom = cosr * cosr + sinhi * sinhi;
return(new Complex(cosr * Trig.HyperbolicCosine(imag) / denom, Trig.Sine(real) * sinhi / denom));
}
