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Showing content from https://en.cppreference.com/w/cpp/language/../memory/../language/../numeric/complex/sqrt.html below:

std::sqrt(std::complex) - cppreference.com

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

[edit] Parameters z - complex number to take the square root of [edit] 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; +â) along the real axis and (ââ; +â) along the imaginary axis).

[edit] 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 (Â±0,+0), the result is (+0,+0)
If z is (x,+â), the result is (+â,+â) even if x is NaN
If z is (x,NaN), the result is (NaN,NaN) (unless x is Â±â) and FE_INVALID may be raised
If z is (-â,y), the result is (+0,+â) for finite positive y
If z is (+â,y), the result is (+â,+0) for finite positive y
If z is (-â,NaN), the result is (NaN,â) (sign of imaginary part unspecified)
If z is (+â,NaN), the result is (+â,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)

[edit] Notes

The semantics of this function are intended to be consistent with the C function csqrt.

[edit] 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";
}

Output:

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

[edit] 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 imaginary parts erroneous requirement removed [edit] See also

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