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Showing content from https://en.cppreference.com/w/cpp/language/../error/error_code/../../numeric/complex/cosh.html below:

std::cosh(std::complex) - cppreference.com

template< class T > complex<T> cosh( const complex<T>& z );

(since C++11)

Computes complex hyperbolic cosine of a complex value z.

[edit] Parameters [edit] Return value

If no errors occur, complex hyperbolic cosine of z is returned.

[edit] Error handling and special values

Errors are reported consistent with math_errhandling.

If the implementation supports IEEE floating-point arithmetic,

std::cosh(std::conj(z)) == std::conj(std::cosh(z))
std::cosh(z) == std::cosh(-z)
If z is (+0,+0), the result is (1,+0)
If z is (+0,+â), the result is (NaN,Â±0) (the sign of the imaginary part is unspecified) and FE_INVALID is raised
If z is (+0,NaN), the result is (NaN,Â±0) (the sign of the imaginary part is unspecified)
If z is (x,+â) (for any finite non-zero x), the result is (NaN,NaN) and FE_INVALID is raised
If z is (x,NaN) (for any finite non-zero x), the result is (NaN,NaN) and FE_INVALID may be raised
If z is (+â,+0), the result is (+â,+0)
If z is (+â,y) (for any finite non-zero y), the result is +âcis(y)
If z is (+â,+â), the result is (Â±â,NaN) (the sign of the real part is unspecified) and FE_INVALID is raised
If z is (+â,NaN), the result is (+â,NaN)
If z is (NaN,+0), the result is (NaN,Â±0) (the sign of the imaginary part is unspecified)
If z is (NaN,+y) (for any finite non-zero 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 cosine is

cosh z =

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.

[edit] Examples

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)

[edit] See also

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