std::sqrt(std::complex)

 

C++

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std::complex

Member functions
complex::complex
complex::operator=
complex::real
complex::imag
complex::operator+=complex::operator-=complex::operator*=complex::operator/=
Non-member functions
operator+operator- operator+operator-operator*operator/ operator==operator!= (until C++20) operator<<operator>>	real imag abs arg norm conj proj (C++11) polar operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
Exponential functions
exp
log
log10
Power functions
pow
sqrt
Trigonometric functions
sin cos tan	asin (C++11) acos (C++11) atan (C++11)
Hyperbolic functions
sinh cosh tanh	asinh (C++11) acosh (C++11) atanh (C++11)

 

Defined in header <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

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 <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';
}

Output:

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

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

See also

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