NAME

csqrt — complex square root function

SYNOPSIS

#include <complex.h>

double complex
csqrt(double complex z);

long double complex
csqrtl(long double complex z);

float complex
csqrtf(float complex z);

DESCRIPTION

csqrt(z) computes the square root of the complex floating-point number z, with a branch cut on the negative real axis. The result is in the right half-plane, including the imaginary axis. For all complex z, csqrt(conj(z)) = conj(csqrt(z)).

SPECIAL VALUES

The conjugate symmetry of csqrt() is used to abbreviate the specification of special values.

csqrt(±0 + 0i) returns +0 + 0i.

csqrt(x + inf i) returns inf + inf i for all x (including NaN).

csqrt(x + NaN i) returns NaN + NaN i.

csqrt(-inf + yi) returns 0 + inf i for any positively-signed finite y.

csqrt(inf + yi) returns inf + 0i for any positively-signed finite y.

csqrt(-inf + NaN i) returns NaN + inf i.

csqrt(inf + NaN i) returns inf + NaN i.

csqrt(NaN + yi) returns NaN + NaN i.

csqrt(NaN + NaN i) returns NaN + NaN i.

NOTES

If z is in the upper half-plane, then csqrt(z) is in the upper-right quadrant of the complex plane. If z is in the lower half-plane, then csqrt(z) is in the lower-right quadrant of the complex plane.

STANDARDS