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
See Wikipedia for more information on complex numbers.

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:


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.