# csqrtf, csqrt, csqrtl

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< c‎ | numeric‎ | complex

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

Run this code

    #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

### 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)

### See also

cpow cpowf cpowl (C99)(C99)(C99) | computes the complex power function (function)
sqrt sqrtf sqrtl (C99)(C99) | computes square root (√x) (function)

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