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