< cpp‎ | numeric‎ | 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.


[edit] Parameters

z - complex value

[edit] Return value

Complex arc tangent of z in the range [−iπ/2 ; +iπ/2] along the imaginary axis.

[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 = -
i [ln(1 - iz) - ln (1 + iz]

[edit] Example

#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';


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)

[edit] See also

computes arc sine of a complex number (arcsin(z))
(function template) [edit]
computes arc cosine of a complex number (arccos(z))
(function template) [edit]
computes tangent of a complex number (tan(z))
(function template) [edit]
computes arc tangent (arctan(x))
(function) [edit]
applies the function std::atan to each element of valarray
(function template) [edit]
C documentation for catan