std::atan(std::complex)
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std::complex
(until C++20)
(C++26)
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(C++26)
Defined in header
<complex>
template< class T >
complex<T> atan( const complex<T>& z );
(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.
Contents
[edit] Parameters
z
-
complex value
[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 [−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.
[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 (-∞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)].
[edit] 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)
[edit] See also
(C++11)
(function template) [edit]
(C++11)
(function template) [edit]
C documentation for catan