The Excel IMPRODUCT Function

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Related Function :

IMDIV Function

Multiplying Complex Numbers

When multiplying two complex numbers a+bi and c+di, the formula used is as follows:

(a+bi) * (c+di) = (ac-bd) + (ad+bc)i

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

Basic Description

The Excel IMPRODUCT function calculates the product of two or more complex numbers.

The format of the function is :

IMPRODUCT( Inumber1, Inumber2, ... )

where the Inumber1, Inumber2, ... arguments are between 2 and 29 supplied Complex Numbers.

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 arguments can be supplied to the Excel Improduct 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.

Examples

In the example below, the Excel Improduct function is used find the product of different complex numbers.

The functions are shown in the spreadsheet on the left and the results are shown in the spreadsheet on the right.

Formulas

	A	B
1	1-i	=IMPRODUCT( A1, A2 )
2	5+10i	=IMPRODUCT( "1-i", "5+10i", 2 )
3		=IMPRODUCT( COMPLEX( 5, 2 ), COMPLEX( 0, 1 ) )

Results

	A	B
1	1-i	15+5i
2	5+10i	30+10i
3		-2+5i

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

Common Errors

If you get an error from your Excel Improduct function this is likely to be one of the following :

#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.

To do this in Excel 2003 :

From the Tools drop-down menu, select the option Add-Ins ...
An 'Add-Ins' window will pop up. From this, select the option Analysis ToolPak and click OK

To do this in Excel 2007 :

Click the Microsoft button on the top left of your spreadsheet and select the Excel Options button
From the menu on the left hand side, select Add-Ins
In the 'Manage:' box, select Excel Add-ins and click Go...
An 'Add-Ins' window will pop up. From this, select the option Analysis ToolPak and click OK