# csqrtf, csqrt, csqrtl

< c‎ | numeric‎ | complex

Complex number arithmetic
Types and the imaginary constant
 complex(C99) _Complex_I(C99) CMPLX(C11)
 imaginary(C99) _Imaginary_I(C99) I(C99)
Manipulation
 cimag(C99) creal(C99) carg(C99)
 cabs(C99) conj(C99) cproj(C99)
Power and exponential functions
 cexp(C99) clog(C99)
 cpow(C99) csqrt(C99)
Trigonometric functions
 ccos(C99) csin(C99) ctan(C99)
 cacos(C99) casin(C99) catan(C99)
Hyperbolic functions
 ccosh(C99) csinh(C99) ctanh(C99)
 cacosh(C99) casinh(C99) catanh(C99)

 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±∞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

### 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

 cpowcpowfcpowl(C99)(C99)(C99) computes the complex power function (function)  sqrtsqrtfsqrtl(C99)(C99) computes square root (√x) (function)  C++ documentation for sqrt