# 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: For further information on Complex Numbers, see the Wikipedia Complex Numbers Page.

## Function Description

The Excel Imabs function returns the absolute value (the modulus) of a complex number.

The syntax of the function is:

IMABS( inumber )

where the inumber argument is a Complex Number.

### 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.

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

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

## Excel Imabs Function Examples

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

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

Note that, in the above example spreadsheet:

• The integer 6, used in cell B3, is equal to the complex number 6+0i;
• The example in cell B5 uses the Excel Complex Function to create the complex number 4+i.

Further details on the Excel Imabs function are provided 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. #VALUE! - Occurs if the supplied inumber argument is a logical value.