std::atan(std::complex) (3) - Linux Manuals

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

NAME

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)