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std::sqrt(std::complex)

From cppreference.com
< cpp‎ | numeric‎ | complex
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.

Contents

[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; +∞) along the real axis and (−∞; +∞) 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 (±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)

[edit] Notes

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

[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] 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';
}

Output:

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

[edit] See also

complex power, one or both arguments may be a complex number
(function template) [edit]
computes square root (x)
(function) [edit]
applies the function std::sqrt to each element of valarray
(function template) [edit]
C documentation for csqrt