std::atan(std::complex)(3)

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 <cmath>
 #include <complex>
 #include <iostream>
 int main()
 {
     std::cout << std::fixed;
     std::complex<double> z1(0.0, 2.0);
     std::cout << "atan" << z1 << " = " << std::atan(z1) << '\n';
     std::complex<double> z2(-0.0, 2.0);
     std::cout << "atan" << z2 << " (the other side of the cut) = "
               << std::atan(z2) << '\n';
     std::complex<double> z3(0.0, 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)

See also
   asin(std::complex) computes arc sine of a complex number
   (C++11) (\({\small\arcsin{z}}\)arcsin(z))
                       (function template)
   acos(std::complex) computes arc cosine of a complex number
   (C++11) (\({\small\arccos{z}}\)arccos(z))
                       (function template)
   tan(std::complex) computes tangent of a complex number (\({\small\tan{z}}\)tan(z))
                       (function template)
   atan
   atanf computes arc tangent (\({\small\arctan{x}}\)arctan(x))
   atanl (function)
   (C++11)
   (C++11)
   atan(std::valarray) applies the function std::atan to each element of valarray
                       (function template)
   C documentation for
   catan