# The Excel IMAGINARY Function

Related Function:
IMREAL Function

Complex Numbers

Within the world of complex numbers, the 'imaginary' value, i is used to represent the square root of -1.

A Complex Number is composed of a real number combined with an imaginary number.

E.g. The complex number, z, is written as

z   =   5 + 2i

## Basic Description

The Excel IMAGINARY function returns the imaginary coefficient of a supplied complex number

- i.e. for the complex number a + bi, the Excel Imaginary function returns the value b.

The syntax of the function is :

IMAGINARY( 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 Imaginary function as any of the following:

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

These are all included in the examples below.

## Excel Imaginary Function Examples

In the example below, the Excel Imaginary function is used find the imaginary coefficient of different complex numbers.

Formulas:
AB
15+2i=IMAGINARY( A1 )
2 =IMAGINARY( "2-i" )
3 =IMAGINARY( 6 )
4 =IMAGINARY( "3i" )
5 =IMAGINARY( COMPLEX( 4, 1 ) )
Results:
AB
15+2i2
2 -1
3 0
4 3
5 1

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

## Imaginary Function Errors

If you get an error from the Excel Imaginary 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.