# std::cosh(std::complex)

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< cpp‎ | numeric‎ | complex

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.

### Parameters

z | - | complex value

### Return value

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

### 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,+∞)`, the result is `(NaN,±0)` (the sign of the imaginary part is unspecified) and FE_INVALID is raised
- If z is `(+0,NaN)`, the result is `(NaN,±0)` (the sign of the imaginary part is unspecified)
- If z is `(x,+∞)` (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 `(+∞,+0)`, the result is `(+∞,+0)`
- If z is `(+∞,y)` (for any finite non-zero 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)`
- If z is `(NaN,+0)`, the result is `(NaN,±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).

### Notes

Mathematical definition of hyperbolic cosine is cosh z =

ez +e-z
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.

### Examples

Run this code

    #include <cmath>
    #include <complex>
    #include <iostream>

    int main()
    {
        std::cout << std::fixed;
        std::complex<double> z(1.0, 0.0); // 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(0.0, 1.0); // 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)

### See also

sinh(std::complex) | computes hyperbolic sine of a complex number (\({\small\sinh{z} }\)sinh(z)) (function template)
tanh(std::complex) | computes hyperbolic tangent of a complex number (\({\small\tanh{z} }\)tanh(z)) (function template)
acosh(std::complex) (C++11) | computes area hyperbolic cosine of a complex number (\({\small\operatorname{arcosh}{z} }\)arcosh(z)) (function template)
cosh coshf coshl (C++11)(C++11) | computes hyperbolic cosine (\({\small\cosh{x} }\)cosh(x)) (function)
cosh(std::valarray) | applies the function std::cosh to each element of valarray (function template)

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