std::atan(std::complex)

 

C++

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Technical Specifications

 

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std::complex

Member functions
complex::complex
complex::operator=
complex::real
complex::imag
complex::operator+=complex::operator-=complex::operator*=complex::operator/=
Non-member functions
operator+operator- operator+operator-operator*operator/ operator==operator!= operator<<operator>>	real imag abs arg norm conj proj (C++11) polar operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
Exponential functions
exp
log
log10
Power functions
pow
sqrt
Trigonometric functions
sin cos tan	asin (C++11) acos (C++11) atan (C++11)
Hyperbolic functions
sinh cosh tanh	asinh (C++11) acosh (C++11) atanh (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

Complex arc tangent of z in the range [−iπ/2 ; +iπ/2] along the imaginary axis.

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)
atan	computes arc tangent (arctan(x)) (function)
atan(std::valarray)	applies the function std::atan to each element of valarray (function template)
C documentation for catan