casin.c File Reference

#include "prim.h"

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Functions
complex	casin (complex z)
	Inverse sine of complex number. More...

Function Documentation

casin()

complex casin

(

complex

z

)

Inverse sine of complex number.

Inverse sine expressed using complex logarithms:

arcsin z = -i * log(iz + sqrt(1 - z*z))

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

Definition at line 42 of file casin.c.

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

Referenced by ComplexNumber::ArcSine().

{
    complex one = cpack(1.0, 0.0);
    complex i = cpack(0.0, 1.0);
    complex j = cpack(0.0, -1.0);
    complex iz = cmul(i, z);
    complex z2 = cmul(z, z);
    complex p = csqrt(csub(one, z2));
    complex q = clog(cadd(iz, p));
    complex w = cmul(j, q);
    return w;
}

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