# csqrtf, csqrt, csqrtl

< c‎ | numeric‎ | complex

C
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Complex number arithmetic
Types and the imaginary constant
Manipulation
Power and exponential functions
 cpow csqrt
Trigonometric functions
Hyperbolic functions

 Defined in header `` 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 `` #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.

## Contents

### 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±∞` (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```