/C

# csqrtf, csqrt, csqrtl

Defined in header `<complex.h>`
`float complex       csqrtf( float complex z );`
(1) (since C99)
`double complex      csqrt( double complex z );`
(2) (since C99)
`long double complex csqrtl( long double complex z );`
(3) (since C99)
Defined in header `<tgmath.h>`
`#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.

### Parameters

 z - complex argument

### 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; +∞) along the real axis and (−∞; +∞) along the imaginary axis.).

### 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 `±0+0i`, the result is `+0+0i`
• If `z` is `x+∞i`, the result is `+∞+∞i` even if x is NaN
• If `z` is `x+NaNi`, the result is `NaN+NaNi` (unless x is ±∞) and `FE_INVALID` may be raised
• If `z` is `-∞+yi`, the result is `+0+∞i` for finite positive y
• If `z` is `+∞+yi`, the result is `+∞+0i)` for finite positive y
• If `z` is `-∞+NaNi`, the result is `NaN±∞i` (sign of imaginary part unspecified)
• If `z` is `+∞+NaNi`, the result is `+∞+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`

### 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```
• 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)