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:

Formula for the modulus of a complex number

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.

  A B
1 5+2i =IMABS( A1 )
2   =IMABS( "2+2i" )
3   =IMABS( 6 )
4   =IMABS( "3i" )
5   =IMABS( COMPLEX( 4, 1 ) )
  A B
1 5+2i 5.385164807
2   2.828427125
3   6
4   3
5   4.123105626

Note that, in the above example spreadsheet:

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.