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Defined in header <complex> | ||
template<class T> complex<T> atan(const complex<T>& z); | (since C++11) | |
Computes complex arc tangent of a complex valuez. Branch cut exists outside the interval[−i, +i] along the imaginary axis.
Contents |
| z | - | complex value |
If no errors occur, complex arc tangent ofz 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), wherei is the imaginary unit.
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 isatan z = -| 1 |
| 2 |
#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)
(C++11) | computes arc sine of a complex number (\({\small\arcsin{z}}\)arcsin(z)) (function template)[edit] |
(C++11) | computes arc cosine of a complex number (\({\small\arccos{z}}\)arccos(z)) (function template)[edit] |
| computes tangent of a complex number (\({\small\tan{z}}\)tan(z)) (function template)[edit] | |
(C++11)(C++11) | computes arc tangent (\({\small\arctan{x}}\)arctan(x)) (function)[edit] |
| applies the functionstd::atan to each element of valarray (function template)[edit] | |
C documentation forcatan | |
