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FreeBSD 11.0 - man page for csqrt (freebsd section 3)

CSQRT(3)						   BSD Library Functions Manual 						  CSQRT(3)

csqrt, csqrtf, csqrtl -- complex square root functions
Math Library (libm, -lm)
#include <complex.h> double complex csqrt(double complex z); float complex csqrtf(float complex z); long double complex csqrtl(long double complex z);
The csqrt(), csqrtf(), and csqrtl() functions compute the square root of z in the complex plane, with a branch cut along the negative real axis. In other words, csqrt(), csqrtf(), and csqrtl() always return the square root whose real part is non-negative.
These functions return the requested square root. The square root of 0 is +0 +- 0, where the imaginary parts of the input and respective result have the same sign. For infinities and NaNs, the following rules apply, with the earlier rules having precedence: Input Result k + infinity*I infinity + infinity*I (for all k) -infinity + NaN*I NaN +- infinity*I infinity + NaN*I infinity + NaN*I k + NaN*I NaN + NaN*I NaN + k*I NaN + NaN*I -infinity + k*I +0 + infinity*I infinity + k*I infinity + 0*I For numbers with negative imaginary parts, the above special cases apply given the identity: csqrt(conj(z) = conj(sqrt(z)) Note that the sign of NaN is indeterminate. Also, if the real or imaginary part of the input is finite and an NaN is generated, an invalid exception will be thrown.
cabs(3), fenv(3), math(3)
The csqrt(), csqrtf(), and csqrtl() functions conform to ISO/IEC 9899:1999 (``ISO C99'').
For csqrt() and csqrtl(), inexact results are not always correctly rounded.
March 30, 2008 BSD