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Showing content from https://en.cppreference.com/w/cpp/language/../algorithm/../ranges/../numeric/complex/atan.html below:

std::atan(std::complex) - cppreference.com

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 [âi, +i] along the imaginary axis.

[edit] Parameters [edit] 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 [âÏ/2, +Ï/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.

[edit] 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 (-âi,-i) and (+i,+âi) of the imaginary axis.

The mathematical definition of the principal value of inverse tangent is

atan z = - i [ln(1 - iz) - ln (1 + iz)]

[edit] Example

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)

[edit] See also

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