# The Excel IMABS Function

Modulus of a Complex Number

The absolute value (the modulus) of a complex number is calculated as the square root of the sum of the squares of the real and imaginary coefficients.

i.e. the modulus of the complex number, z = a + bi is :

Further information on Complex Numbers can be found on the Wikipedia Complex Numbers Page.

## Basic Description

The Excel IMABS function Returns the absolute value (the modulus) of a complex number.

The format of the function is :

IMABS( 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 Imabs 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

These are all included in the examples below.

## Excel Imabs Function Examples

In the example below, the Excel Imabs function is used find the absolute value (the modulus) of different complex numbers.

The format of the function is shown in the spreadsheet on the left and the results are shown in the spreadsheet on the right.

Formulas:
AB
15+2i=IMABS( A1 )
2 =IMABS( "2+2i" )
3 =IMABS( 6 )
4 =IMABS( "3i" )
5 =IMABS( COMPLEX( 4, 1 ) )
Results:
AB
15+2i5.385164807
2 2.828427125
3 6
4 3
5 4.123105626

Further information on the Excel Imabs function can be found on the Microsoft Office website.

## Imabs Function Errors

If you get an error from the Imabs 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.