# ccoshf, ccosh, ccoshl

< c‎ | numeric‎ | complex

C
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Complex number arithmetic
Types and the imaginary constant
Manipulation
Power and exponential functions
Trigonometric functions
Hyperbolic functions
 ccosh csinh ctanh

 Defined in header `` float complex       ccoshf( float complex z ); (1) (since C99) double complex      ccosh( double complex z ); (2) (since C99) long double complex ccoshl( long double complex z ); (3) (since C99) Defined in header `` #define cosh( z ) (4) (since C99)
1-3) Computes the complex hyperbolic cosine of `z`.
4) Type-generic macro: If `z` has type long double complex, `ccoshl` is called. if `z` has type double complex, `ccosh` is called, if `z` has type float complex, `ccoshf` is called. If `z` is real or integer, then the macro invokes the corresponding real function (coshf, cosh, coshl). If `z` is imaginary, then the macro invokes the corresponding real version of the function cos, implementing the formula cosh(iy) = cos(y), and the return type is real.

### Parameters

 z - complex argument

### 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,

• ccosh(conj(z)) == conj(ccosh(z))
• ccosh(z) == ccosh(-z)
• If `z` is `+0+0i`, the result is `1+0i`
• If `z` is `+0+∞i`, the result is `NaN±0i` (the sign of the imaginary part is unspecified) and FE_INVALID is raised
• If `z` is `+0+NaNi`, the result is `NaN±0i` (the sign of the imaginary part is unspecified)
• If `z` is `x+∞i` (for any finite non-zero x), the result is `NaN+NaNi` and FE_INVALID is raised
• If `z` is `x+NaNi` (for any finite non-zero x), the result is `NaN+NaNi` and FE_INVALID may be raised
• If `z` is `+∞+0i`, the result is `+∞+0i`
• If `z` is `+∞+yi` (for any finite non-zero y), the result is `+∞+cis(y)`
• If `z` is `+∞+∞i`, the result is `±∞+NaNi` (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+0i`, the result is `NaN±0i` (the sign of the imaginary part is unspecified)
• If `z` is `NaN+yi` (for any finite non-zero y), the result is `NaN+NaNi` and FE_INVALID may be raised
• If `z` is `NaN+NaNi`, the result is `NaN+NaNi`

where cis(y) is cos(y) + i sin(y)