Defined in header <complex>  

template< class T > complex<T> tanh( const complex<T>& z );  (since C++11) 
Computes complex hyperbolic tangent of a complex value z
.
z    complex value 
If no errors occur, complex hyperbolic tangent of z
is returned.
Errors are reported consistent with math_errhandling
.
If the implementation supports IEEE floatingpoint arithmetic,
std::tanh(std::conj(z)) == std::conj(std::tanh(z))
std::tanh(z) == std::tanh(z)
z
is (+0,+0)
, the result is (+0,+0)
z
is (x,+∞)
(for any^{[1]} finite x), the result is (NaN,NaN)
and FE_INVALID
is raised z
is (x,NaN)
(for any^{[2]} finite x), the result is (NaN,NaN)
and FE_INVALID
may be raised z
is (+∞,y)
(for any finite positive y), the result is (1,+0)
z
is (+∞,+∞)
, the result is (1,±0)
(the sign of the imaginary part is unspecified) z
is (+∞,NaN)
, the result is (1,±0)
(the sign of the imaginary part is unspecified) z
is (NaN,+0)
, the result is (NaN,+0)
z
is (NaN,y)
(for any nonzero y), the result is (NaN,NaN)
and FE_INVALID
may be raised z
is (NaN,NaN)
, the result is (NaN,NaN)
z
is (0,∞)
, the result should be (0,NaN)
z
is (0,NaN)
, the result should be (0,NaN)
Hyperbolic tangent is an analytical function on the complex plane and has no branch cuts. It is periodic with respect to the imaginary component, with period πi, and has poles of the first order along the imaginary line, at coordinates (0, π(1/2 + n)). However no common floatingpoint representation is able to represent π/2 exactly, thus there is no value of the argument for which a pole error occurs.
#include <iostream> #include <cmath> #include <complex> int main() { std::cout << std::fixed; std::complex<double> z(1, 0); // behaves like real tanh along the real line std::cout << "tanh" << z << " = " << std::tanh(z) << " (tanh(1) = " << std::tanh(1) << ")\n"; std::complex<double> z2(0, 1); // behaves like tangent along the imaginary line std::cout << "tanh" << z2 << " = " << std::tanh(z2) << " ( tan(1) = " << std::tan(1) << ")\n"; }
Output:
tanh(1.000000,0.000000) = (0.761594,0.000000) (tanh(1) = 0.761594) tanh(0.000000,1.000000) = (0.000000,1.557408) ( tan(1) = 1.557408)
computes hyperbolic sine of a complex number (\({\small\sinh{z} }\)sinh(z)) (function template) 

computes hyperbolic cosine of a complex number (\({\small\cosh{z} }\)cosh(z)) (function template) 

(C++11)  computes area hyperbolic tangent of a complex number (\({\small\operatorname{artanh}{z} }\)artanh(z)) (function template) 
(C++11)(C++11)  computes hyperbolic tangent (\({\small\tanh{x} }\)tanh(x)) (function) 
applies the function std::tanh to each element of valarray (function template) 

C documentation for ctanh 
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