Std::atan(std::complex) (3) Linux Manual Page

std::atan(std::complex) – std::atan(std::complex)

Synopsis

Defined in header<complex>

    template <class T>
    (since C++ 11)

        complex<T> atan(const complex<T> &z);

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

Parameters

z – complex value

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.

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)]

Example

// Run this code

#include <iostream>

#include <complex>

#include <cmath>

int main()

{
    std::cout << std::fixed;
    std::complex<double> z1(0, 2);
    std::cout << "atan" << z1 << " = " << std::atan(z1) << '\n';
    std::complex<double> z2(-0.0, 2);
    std::cout << "atan" << z2 << " (the other side of the cut) = "
              << std::atan(z2) << '\n';
    std::complex<double> z3(0, INFINITY);
    std::cout << "2*atan" << z3 << " = " << 2.0 * std::atan(z3) << '\n';
}

Output:

  atan(0.000000,2.000000) = (1.570796,0.549306)
  atan(-0.000000,2.000000) (the other side of the cut) = (-1.570796,0.549306)
  2*atan(0.000000,inf) = (3.141593,0.000000)

asin(std::complex) computes arc sine of a complex number (arcsin(z))
                    (function template)
(C++11)
acos(std::complex) computes arc cosine of a complex number (arccos(z))
                    (function template)
(C++11)
                    computes tangent of a complex number (tan(z))
tan(std::complex) (function template)
atan
atanf
atanl computes arc tangent (arctan(x))
                    (function)
(C++11)
(C++11)
                    applies the function std::atan to each element of valarray
atan(std::valarray) (function template)

std::atan(std::complex) (3) Linux Manual Page