# std::atan(std::complex)

From cppreference.com
< 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.

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

Retrieved from "https://en.cppreference.com/mwiki/index.php?title=cpp/numeric/complex/atan&oldid=99363"