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.
z    complex number to take the square root of 
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.).
Errors are reported consistent with math_errhandling
.
If the implementation supports IEEE floatingpoint arithmetic,
std::sqrt(std::conj(z)) == std::conj(std::sqrt(z))
z
is (±0,+0)
, the result is (+0,+0)
z
is (x,+∞)
, the result is (+∞,+∞)
even if x is NaN z
is (x,NaN)
, the result is (NaN,NaN)
(unless x is ±∞) and FE_INVALID
may be raised z
is (∞,y)
, the result is (+0,+∞)
for finite positive y z
is (+∞,y)
, the result is (+∞,+0)
for finite positive y z
is (∞,NaN)
, the result is (NaN,∞)
(sign of imaginary part unspecified) z
is (+∞,NaN)
, the result is (+∞,NaN)
z
is (NaN,y)
, the result is (NaN,NaN)
and FE_INVALID
may be raised z
is (NaN,NaN)
, the result is (NaN,NaN)
The semantics of this function are intended to be consistent with the C function csqrt
.
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 
#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)
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) 
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