catan.c File Reference

#include "prim.h"

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Functions
complex	catan (complex z)
	Inverse tangent of complex number. More...

Function Documentation

catan()

complex catan

(

complex

z

)

Inverse tangent of complex number.

Inverse tangent expressed using complex logarithms:

atan(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 catan.c.

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

Referenced by ComplexNumber::ArcTangent().

{
    complex one = cpack(1.0, 0.0);
    complex two = cpack(2.0, 0.0);
    complex i = cpack(0.0, 1.0);
    complex iz = cmul(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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