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std::sqrt(std::complex)

From cppreference.com
< cpp‎ | numeric‎ | complex
 
C++
 
Numerics library
 
std::complex
 
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.

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] Example

Run this code
#include <complex>
#include <iostream>
 
int main()
{
    std::cout << "Square root of -4 is "
              << std::sqrt(