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)

See also¶

asin(std::complex) computes arc sine of a complex number (\({\small\arcsin{z}
(C++11) }\)arcsin(z))
(function template)
acos(std::complex) computes arc cosine of a complex number (\({\small\arccos{z}
(C++11) }\)arccos(z))
(function template)
computes tangent of a complex number (\({\small\tan{z}
tan(std::complex) }\)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)