std::sinh(std::complex)
From cppreference.com
Defined in header <complex>


template< class T > complex<T> sinh( const complex<T>& z ); 
(since C++11)  
Computes complex hyperbolic sine of a complex value z
.
Contents 
[edit] Parameters
z    complex value 
[edit] Return value
If no errors occur, complex hyperbolic sine of z
is returned
[edit] Error handling and special values
Errors are reported consistent with math_errhandling
If the implementation supports IEEE floatingpoint arithmetic,
 std::sinh(std::conj(z)) == std::conj(std::sinh(z))
 std::sinh(z) == std::sinh(z)
 If
z
is(+0,+0)
, the result is(+0,+0)
 If
z
is(+0,+∞)
, the result is(±0,NaN)
(the sign of the real part is unspecified) and FE_INVALID is raised  If
z
is(+0,NaN)
, the result is(±0,NaN)
 If
z
is(x,+∞)
(for any positive finite x), the result is(NaN,NaN)
and FE_INVALID is raised  If
z
is(x,NaN)
(for any positive finite x), the result is(NaN,NaN)
and FE_INVALID may be raised  If
z
is(+∞,+0)
, the result is(+∞,+0)
 If
z
is(+∞,y)
(for any positive finite y), the result is+∞cis(y)
 If
z
is(+∞,+∞)
, the result is(±∞,NaN)
(the sign of the real part is unspecified) and FE_INVALID is raised  If
z
is(+∞,NaN)
, the result is(±∞,NaN)
(the sign of the real part is unspecified)  If
z
is(NaN,+0)
, the result is(NaN,+0)
 If
z
is(NaN,y)
(for any finite nonzero y), the result is(NaN,NaN)
and FE_INVALID may be raised  If
z
is(NaN,NaN)
, the result is(NaN,NaN)
where cis(y) is cos(y) + i sin(y)
[edit] Notes
Mathematical definition of hyperbolic sine is sinh z =ez ez 
2 
Hyperbolic sine 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
[edit] Example
Run this code
#include <iostream> #include <cmath> #include <complex> int main() { std::cout << std::fixed; std::complex<double> z(1, 0); // behaves like real sinh along the real line std::cout << "sinh" << z << " = " << std::sinh(z) << " (sinh(1) = " << std::sinh(1) << ")\n"; std::complex<double> z2(0, 1); // behaves like sine along the imaginary line std::cout << "sinh" << z2 << " = " << std::sinh(z2) << " ( sin(1) = " << std::sin(1) << ")\n"; }
Output:
sinh(1.000000,0.000000) = (1.175201,0.000000) (sinh(1) = 1.175201) sinh(0.000000,1.000000) = (0.000000,0.841471) ( sin(1) = 0.841471)
[edit] See also
computes hyperbolic cosine of a complex number (ch(z)) (function template)  
computes hyperbolic tangent of a complex number (function template)  
(C++11) 
computes area hyperbolic sine of a complex number (function template) 
computes hyperbolic sine (sh(x)) (function)  
applies the function std::sinh to each element of valarray (function template)  
C documentation for csinh
