Defined in header <complex>  

template< class T > complex<T> cosh( const complex<T>& z );  (since C++11) 
Computes complex hyperbolic cosine of a complex value z
.
z    complex value 
If no errors occur, complex hyperbolic cosine of z
is returned.
Errors are reported consistent with math_errhandling
.
If the implementation supports IEEE floatingpoint arithmetic,
std::cosh(std::conj(z)) == std::conj(std::cosh(z))
std::cosh(z) == std::cosh(z)
z
is (+0,+0)
, the result is (1,+0)
z
is (+0,+∞)
, the result is (NaN,±0)
(the sign of the imaginary part is unspecified) and FE_INVALID
is raised z
is (+0,NaN)
, the result is (NaN,±0)
(the sign of the imaginary part is unspecified) z
is (x,+∞)
(for any finite nonzero x), the result is (NaN,NaN)
and FE_INVALID
is raised z
is (x,NaN)
(for any finite nonzero x), the result is (NaN,NaN)
and FE_INVALID
may be raised z
is (+∞,+0)
, the result is (+∞,+0)
z
is (+∞,y)
(for any finite nonzero y), the result is +∞cis(y)
z
is (+∞,+∞)
, the result is (±∞,NaN)
(the sign of the real part is unspecified) and FE_INVALID
is raised z
is (+∞,NaN)
, the result is (+∞,NaN)
z
is (NaN,+0)
, the result is (NaN,±0)
(the sign of the imaginary part is unspecified) z
is (NaN,+y)
(for any finite nonzero y), the result is (NaN,NaN)
and FE_INVALID
may be raised z
is (NaN,NaN)
, the result is (NaN,NaN)
where cis(y) is cos(y) + i sin(y).
ez +ez 
2 
Hyperbolic cosine is an entire function in the complex plane and has no branch cuts. It is periodic with respect to the imaginary component, with period 2πi.
#include <iostream> #include <cmath> #include <complex> int main() { std::cout << std::fixed; std::complex<double> z(1, 0); // behaves like real cosh along the real line std::cout << "cosh" << z << " = " << std::cosh(z) << " (cosh(1) = " << std::cosh(1) << ")\n"; std::complex<double> z2(0, 1); // behaves like real cosine along the imaginary line std::cout << "cosh" << z2 << " = " << std::cosh(z2) << " ( cos(1) = " << std::cos(1) << ")\n"; }
Output:
cosh(1.000000,0.000000) = (1.543081,0.000000) (cosh(1) = 1.543081) cosh(0.000000,1.000000) = (0.540302,0.000000) ( cos(1) = 0.540302)
computes hyperbolic sine of a complex number (sh(z)) (function template) 

computes hyperbolic tangent of a complex number (function template) 

(C++11)  computes area hyperbolic cosine of a complex number (function template) 
(C++11)(C++11)  computes hyperbolic cosine (ch(x)) (function) 
applies the function std::cosh to each element of valarray (function template) 
© cppreference.com
Licensed under the Creative Commons AttributionShareAlike Unported License v3.0.
http://en.cppreference.com/w/cpp/numeric/complex/cosh