cacot.c File Reference

#include "prim.h"

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Functions
complex	cacot (complex z)
	Inverse cotangent of complex number. More...

Function Documentation

cacot()

complex cacot

(

complex

z

)

Inverse cotangent of complex number.

Inverse cotangent expressed using complex logarithms:

arccot z = i/2 * (log(1 - i/z) - log(1 + i/z))

More info is available at Wikipedia:
https://wikipedia.org/wiki/Inverse_trigonometric_functions#Logarithmic_forms

Definition at line 42 of file cacot.c.

References cadd(), cdiv(), clog(), cmul(), cpack(), and csub().

Referenced by ComplexNumber::ArcCotangent().

{
    complex one = cpack(1.0, 0.0);
    complex two = cpack(2.0, 0.0);
    complex i = cpack(0.0, 1.0);
    complex iz = cdiv(i, z);
    complex p = clog(csub(one, iz));
    complex q = clog(cadd(one, iz));
    complex w = cmul(cdiv(i, two), csub(p, q));
    return w;
}

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