std::atan(std::complex)

 

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std::complex

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complex::complex complex::operator= complex::real complex::imag	complex::operator+=complex::operator-=complex::operator*=complex::operator/=
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operator+operator- operator+operator-operator*operator/ operator==operator!= (until C++20)   operator<<operator>> get(std::complex) (C++26)	real imag abs arg norm conj proj (C++11) polar operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
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log   log10   exp
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sin   cos tan asin (C++11) acos (C++11) atan (C++11)
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sinh   cosh tanh asinh (C++11) acosh (C++11) atanh (C++11)
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tuple_size<std::complex> (C++26)
tuple_element<std::complex> (C++26)

 

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 <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

asin(std::complex) (C++11)	computes arc sine of a complex number (\({\small\arcsin{z}}\)arcsin(z)) (function template)
acos(std::complex) (C++11)	computes arc cosine of a complex number (\({\small\arccos{z}}\)arccos(z)) (function template)
tan(std::complex)	computes tangent of a complex number (\({\small\tan{z}}\)tan(z)) (function template)
atanatanfatanl (C++11)(C++11)	computes arc tangent (\({\small\arctan{x}}\)arctan(x)) (function)
atan(std::valarray)	applies the function std::atan to each element of valarray (function template)
C documentation for catan