# The Excel IMCOS Function

Related Function:
IMSIN Function
Cosine of a Complex Number

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

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

## Basic Description

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

The format of the function is:

IMCOS( 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.

Therefore, the inumber argument can be supplied to the Excel Imcos function as either:

• A simple number
or
• A complex number encased in quotation marks - eg. "5+3i"
or
• A reference to a cell containing a complex number or a numeric value
or
• A value returned from another Excel function or formula

## Imcos Function Examples

The spreadsheet below shows 4 different examples of the Imcos function.

The format of the functions are shown in the spreadsheet on the left and the resulting values are shown in the spreadsheet on the right.

Formulas:
AB
1 =IMCOS( 0.5 )
2 =IMCOS( "3+0.5i" )
32-i=IMCOS( A3 )
4 =IMCOS( COMPLEX( 1, -1 ) )
Results:
AB
1 0.877582561890373
2 -1.11634124452615-0.0735369737112366i
32-i-0.64214812471552+1.06860742138278i
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.

Further information and examples of the Excel Imcos function can be found on the Microsoft Office website

## Imcos Function Errors

If you get an error from the Excel Imcos 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 #NAME? - Occurs when Analysis ToolPak add-in is not enabled in your Excel.You will need to enable the add-in if you want to use the Excel complex number functions.