std::atan(std::complex)

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< cpp‎ | numeric‎ | complex
 
 
 
std::complex
Member functions
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Exponential functions
Power functions
Trigonometric functions
(C++11)
(C++11)
atan
(C++11)
Hyperbolic functions
(C++11)
(C++11)
(C++11)
 
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.

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

#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

computes arc sine of a complex number (arcsin(z))
(function template)
computes arc cosine of a complex number (arccos(z))
(function template)
computes tangent of a complex number (tan(z))
(function template)
(C++11)(C++11)
computes arc tangent (arctan(x))
(function)
applies the function std::atan to each element of valarray
(function template)