IMCOSH Function

Basic Description

The Excel Imcosh function returns the hyperbolic cosine of a supplied complex number. Note: the Imcosh function was only introduced in Excel 2013 and so is not available in earlier versions of Excel.

Syntax: IMCOSH( inumber )

where the inumber argument is a complex number. 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

The spreadsheet below shows 4 different examples of the Imcosh function. Each example uses a different method to supply the complex number to the function.

1 =IMCOSH( 0.5 )
2 =IMCOSH( “3+0.5i” )
3 2 – i =IMCOSH( A3 )
4 =IMCOSH( COMPLEX( 1, -1 ) )
1 1.12762596520638
2 8.83520460650099+4.80282508274303i
3 2 – i 2.03272300701967-3.0518977991518i
4 0.833730025131149-0.988897705762865i

Note that, in cell B1 of the above spreadsheet, the supplied inumber argument is the real number 0.5, which is equal to the complex number 0.5+0i.


Imcosh Function Errors

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

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

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