# The Excel IMCOSH Function

Hyperbolic Cosine of a Complex Number

The hyperbolic cosine of a complex number is calculated by the following equation:

cosh(x + yi) = cosh(x) cos(y) - sinh(x) sin(y)i

## Function Description

The Excel Imcosh function returns the hyperbolic cosine of a supplied complex number.

Note: the Imcosh function was only introduced in Excel 2013, so is not available in earlier versions of Excel.

The syntax of the function is:

IMCOSH( inumber )

where the inumber argument is the complex number that you want to calculate the hyperbolic cosine of.

### Complex Numbers in Excel

Note that complex numbers are simply stored as text in Excel. When a text string in the format "a+bi" or "a+bj" is supplied to one of Excel's built-in complex number functions, this is interpreted as a complex number.

Also the complex number functions can accept a simple numeric value, as this is equivalent to a complex number whose imaginary coefficient is equal to 0.

## Imcosh Function Examples

Column B of the following spreadsheet shows 4 different examples of the Imcosh function. Each example uses a different method to supply the complex number to the function.

Formulas:
AB
1 =IMCOSH( 0.5 )
2 =IMCOSH( "3+0.5i" )
32-i=IMCOSH( A3 )
4 =IMCOSH( COMPLEX( 1, -1 ) )
Results:
AB
1 1.12762596520638
2 8.83520460650099 + 4.80282508274303i
32-i2.03272300701967 - 3.0518977991518i
4 0.833730025131149 - 0.988897705762865i

Note that, in the above example spreadsheet:

• The real number 0.5, used in cell B1, is equal to the complex number 0.5+0i;
• The example in cell B4 uses the Excel Complex Function to create the complex number 1-i.

Further details and examples of the Excel Imcosh function are provided on the Microsoft Office website

## Imcosh Function Errors

If you get an error from the Excel Imcosh Function, this is likely to be one of the following:

Common Errors
 #NUM! - Occurs if the supplied inumber argument is not recognised as a complex number. #VALUE! - Occurs if the supplied inumber argument is a logical value.