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Showing content from https://en.cppreference.com/w/cpp/algorithm/../ranges/../../c/header/../numeric/complex/csqrt.html below:

csqrtf, csqrt, csqrtl - cppreference.com

(1) (since C99) (2) (since C99) (3) (since C99)

#define sqrt( z )

(4) (since C99)

1-3) Computes the complex square root of z with branch cut along the negative real axis.

4)

Type-generic macro: If

z

has type

long double complex

csqrtl

is called. if

z

has type

double complex

csqrt

is called, if

z

has type

float complex

csqrtf

is called. If

z

is real or integer, then the macro invokes the corresponding real function (

sqrtf

sqrt

sqrtl

). If

z

is imaginary, the corresponding complex number version is called.

[edit] Parameters [edit] Return value

If no errors occur, returns the square root of z, in the range of the right half-plane, including the imaginary axis ([0; +â) along the real axis and (ââ; +â) along the imaginary axis.)

[edit] Error handling and special values

Errors are reported consistent with math_errhandling

If the implementation supports IEEE floating-point arithmetic,

The function is continuous onto the branch cut taking into account the sign of imaginary part
csqrt(conj(z)) == conj(csqrt(z))
If z is Â±0+0i, the result is +0+0i
If z is x+âi, the result is +â+âi even if x is NaN
If z is x+NaNi, the result is NaN+NaNi (unless x is Â±â) and FE_INVALID may be raised
If z is -â+yi, the result is +0+âi for finite positive y
If z is +â+yi, the result is +â+0i) for finite positive y
If z is -â+NaNi, the result is NaNÂ±âi (sign of imaginary part unspecified)
If z is +â+NaNi, the result is +â+NaNi
If z is NaN+yi, the result is NaN+NaNi and FE_INVALID may be raised
If z is NaN+NaNi, the result is NaN+NaNi

[edit] Example

#include <stdio.h>
#include <complex.h>
 
int main(void)
{
    double complex z1 = csqrt(-4);
    printf("Square root of -4 is %.1f%+.1fi\n", creal(z1), cimag(z1));
 
    double complex z2 = csqrt(conj(-4)); // or, in C11, CMPLX(-4, -0.0)
    printf("Square root of -4-0i, the other side of the cut, is "
           "%.1f%+.1fi\n", creal(z2), cimag(z2));
}

Output:

Square root of -4 is 0.0+2.0i
Square root of -4-0i, the other side of the cut, is 0.0-2.0i

[edit] References

C11 standard (ISO/IEC 9899:2011):

7.3.8.3 The csqrt functions (p: 196)

7.25 Type-generic math <tgmath.h> (p: 373-375)

G.6.4.2 The csqrt functions (p: 544)

G.7 Type-generic math <tgmath.h> (p: 545)

C99 standard (ISO/IEC 9899:1999):

7.3.8.3 The csqrt functions (p: 178)

7.22 Type-generic math <tgmath.h> (p: 335-337)

G.6.4.2 The csqrt functions (p: 479)

G.7 Type-generic math <tgmath.h> (p: 480)

[edit] See also

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