# 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

## Function Description

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

The syntax of the function is:

IMCOS( inumber )

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

## Imcos Function Examples

In the spreadsheets below, the Excel Imcos function is used to calculate the cosine of 4 different complex numbers.

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 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 Imcos function are provided 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. #VALUE! - Occurs if the supplied inumber argument is a logical value.