# std::atan(std::complex) (3) - Linux Man Pages

## NAME

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

## Synopsis

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)