std::sqrt(std::complex)(3)

NAME
std::sqrt(std::complex) - std::sqrt(std::complex)

Synopsis
   Defined in header <complex>
   template< class T >
   std::complex<T> sqrt( const std::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
   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
     * 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.

Example
// Run this code
 #include <complex>
 #include <iostream>
 int main()
 {
     std::cout << "Square root of -4 is "
               << std::sqrt(std::complex<double>(-4.0, 0.0)) << '\n'
               << "Square root of (-4,-0) is "
               << std::sqrt(std::complex<double>(-4.0, -0.0))
               << " (the other side of the cut)\n";
 }

Output:
 Square root of -4 is (0,2)
 Square root of (-4,-0) is (0,-2) (the other side of the cut)
   Defect reports
   The following behavior-changing 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 erroneous requirement
                       imaginary parts removed

See also
   pow(std::complex) complex power, one or both arguments may be a complex number
                       (function template)
   sqrt computes square root (\(\small{\sqrt{x}}\)
   sqrtf √
   sqrtl x)
   (C++11) (function)
   (C++11)
   sqrt(std::valarray) applies the function std::sqrt to each element of valarray
                       (function template)
   C documentation for
   csqrt