std::sqrt(std::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

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.).

If the argument is a negative real number, the result lies on the positive 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)

Example

#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';
}

Square root of -4 is (0,2)
Square root of (-4,-0), the other side of the cut, is (0,-2)

See also