std:: sqrt (std::complex)

Computes the square root of the complex number z with a branch cut along the negative real axis.

Parameters

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

#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";
}

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.

See also