# Documentation/Calc Functions/IMCOSH

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## Function name:

IMCOSH

## Category:

Add-in

## Summary:

Calculates the hyperbolic cosine of a complex number.

## Syntax:

IMCOSH(**ComplexNumber**)

## Returns:

Returns a text string giving the complex number that is the hyperbolic cosine of the complex number passed as argument.

## Arguments:

**ComplexNumber** is a string (in quotation marks) representing a complex number in the form *a+bi* or *a+bj*, or a reference to a cell containing that string, whose hyperbolic cosine is to be determined. *a* and *b* are real numbers.

- If
**ComplexNumber**does not have an imaginary part (*b*equal to 0), the real part can be passed to IMCOSH as a number rather than a string. - If
**ComplexNumber**is not a valid complex number, IMCOSH reports an invalid argument error (Err:502).

## Additional details:

### Details specific to IMCOSH function

For a complex number of the form *a+bi*, IMCOSH implements the following equation:

However, IMCOSH determines if *b*=0 and in this case simply returns cosh(*a*).

### General information about Calc's handling of complex numbers

- A complex number is
**a number that can be expressed in the form**, where*a*+*bi**a*and*b*are real numbers and*i*is a symbol for the imaginary unit, such that*i*^{2}=−1.*a*is known as the real part of the complex number and*b*is known as its imaginary part. - In some disciplines using
*i*to indicate the imaginary unit may be undesirable and, in such cases,**the symbol**. The functions provided by Calc to process complex numbers can use either*j*may be used instead*i*or*j*. - For additional
**general background information**, visit Wikipedia’s Complex number page. - Within Calc,
**a complex number is represented as a string expression**of the form "a+bi" or "a+bj", where*a*and*b*are real numbers. If the complex number happens to be a real number (*b*=0), then it can be represented as either a string expression or a numeric value. Complex number string expressions should not contain any space characters. Examples of valid Calc complex numbers include "2", -6, "2+3i", "3j", "12.34+56.78i", and "1e+23-1e-22j". Calc would not recognize the strings "1+j2", "i+1", and "i+j" as valid complex numbers. - The representation of the complex numbers in strings can have
**up to 15 significant digits**and scientific style is automatically used if needed (visit Wikipedia’s Scientific notation page for more information). The decimal delimiter in complex number string expressions is always a dot, irrespective of locale setting.

## Examples:

Formula | Description | Returns |
---|---|---|

=IMCOSH("1.2-3.4j") | Here the function calculates the hyperbolic cosine of a complex number that has non-zero real and imaginary parts. | -1.75053852987314+0.385729418228941j |

=IMCOSH("-i") | Here the function calculates the hyperbolic cosine of a complex number that has no real part. The result has no imaginary part. | 0.54030230586814 |

=IMCOSH(-1) | Here the function calculates the hyperbolic cosine of a complex number that has no imaginary part. The result has no imaginary part. | 1.54308063481524 |

=IMCOSH(F1) where cell F1 contains the complex number 2-3j. | Here the function calculates the hyperbolic cosine of a complex number that is entered in a cell. | -3.72454550491532-0.511822569987385j |

## Related LibreOffice functions:

## ODF standard:

## Related (or similar) Excel functions:

IMCOSH since v.2013.