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std::atan(std::complex)(3) C++ Standard Libary 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

2024.06.10 http://cppreference.com