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std::atan(std::complex)

From cppreference.com
< cpp‎ | numeric‎ | complex
 
C++
 
Numerics library
 
std::complex
 
Defined in header <complex>
template< class T >
complex<T> atan( const complex<T>& z );
 (since C++11)

Computes complex arc tangent of a complex value z. Branch cut exists outside the interval [−i, +i] along the imaginary axis.

Contents

[edit] Parameters

z - complex value

[edit] Return value

If no errors occur, complex arc tangent of z is returned, in the range of a strip unbounded along the imaginary axis and in the interval [−π/2, +π/2] along the real axis.

Errors and special cases are handled as if the operation is implemented by -i * std::atanh(i * z), where i is the imaginary unit.

[edit] Notes

Inverse tangent (or arc tangent) is a multivalued function and requires a branch cut on the complex plane. The branch cut is conventionally placed at the line segments (-∞i,-i) and (+i,+∞i) of the imaginary axis.

The mathematical definition of the principal value of inverse tangent is atan z = -
1
2
 i [ln(1 - iz) - ln (1 + iz)].

[edit] Example

Run this code
#include <cmath>
#include <complex>
#include <iostream>
 
int main()
{
    std::cout << std::fixed;
    std::complex<double> z1(0.0, 2.0);