std::sqrt(std::complex)
From cppreference.com
| Defined in header <complex>
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| template< class T > complex<T> sqrt( const complex<T>& z ); |
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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.)
If the argument is a negative real number, the result lies on the positive 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
zis(±0,+0), the result is(+0,+0) - If
zis(x,+∞), the result is(+∞,+∞)even if x is NaN - If
zis(x,NaN), the result is(NaN,NaN)(unless x is ±∞) and FE_INVALID may be raised - If
zis(-∞,y), the result is(+0,+∞)for finite positive y - If
zis(+∞,y), the result is(+∞,+0)for finite positive y - If
zis(-∞,NaN), the result is(NaN,∞)(sign of imaginary part unspecified) - If
zis(+∞,NaN), the result is(+∞,NaN) - If
zis(NaN,y), the result is(NaN,NaN)and FE_INVALID may be raised - If
zis(NaN,NaN), the result is(NaN,NaN)
[edit] 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)
[edit] See also
| complex power, one or both arguments may be a complex number (function template) | |
| computes square root (√x) (function) | |
| applies the function std::sqrt to each element of valarray (function template) | |
| C documentation for csqrt
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