std::sqrt(std::complex)
From cppreference.com
Defined in header <complex>


template< class T > complex<T> sqrt( const complex<T>& z ); 

Computes the square root of the complex number z
with a branch cut along the negative real axis.
Parameters
z    complex number to take the square root of 
Return value
If no errors occur, returns the square root of z
, in the range of the right halfplane, 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 floatingpoint arithmetic,
 The function is continuous onto the branch cut taking into account the sign of imaginary part
 std::sqrt(std::conj(z)) == std::conj(std::sqrt(z))
 If
z
is(±0,+0)
, the result is(+0,+0)
 If
z
is(x,+∞)
, the result is(+∞,+∞)
even if x is NaN  If
z
is(x,NaN)
, the result is(NaN,NaN)
(unless x is ±∞) and FE_INVALID may be raised  If
z
is(∞,y)
, the result is(+0,+∞)
for finite positive y  If
z
is(+∞,y)
, the result is(+∞,+0)
for finite positive y  If
z
is(∞,NaN)
, the result is(NaN,∞)
(sign of imaginary part unspecified)  If
z
is(+∞,NaN)
, the result is(+∞,NaN)
 If
z
is(NaN,y)
, the result is(NaN,NaN)
and FE_INVALID may be raised  If
z
is(NaN,NaN)
, the result is(NaN,NaN)
Notes
The semantics of this function are intended to be consistent with the C function csqrt.
Defect reports
The following behaviorchanging defect reports were applied retroactively to previously published C++ standards.
DR  Applied to  Behavior as published  Correct behavior 

LWG 2597  C++98  specification mishandles signed zero imaginary parts  erroneous requirement removed 
Example
Run this code
#include <iostream> #include <complex> int main() { std::cout << "Square root of 4 is " << std::sqrt(std::complex<double>(4, 0)) << '\n' << "Square root of (4,0), the other side of the cut, is " << std::sqrt(std::complex<double>(4, 0.0)) << '\n'; }
Output:
Square root of 4 is (0,2) Square root of (4,0), the other side of the cut, is (0,2)
See also
complex power, one or both arguments may be a complex number (function template)  
(C++11)(C++11) 
computes square root (√x) (function) 
applies the function std::sqrt to each element of valarray (function template) 