The Excel IMPRODUCT Function

Related Function:
IMDIV Function
Multiplying Complex Numbers

The formula used to multiply two complex numbers a+bi and c+di is:

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

Complex Numbers are explained in detail on the Wikipedia Complex Numbers Page.

Function Description

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

The syntax of the function is:

IMPRODUCT( inumber1, inumber2, ... )

where the inumber arguments are between 2 and 255 Complex Numbers that you want to find the product of.

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 arguments can be supplied to the Excel Improduct function as either:

• Simple numbers;
• Complex numbers encased in quotation marks - e.g. "5+3i";
• References to cells containing complex numbers or numeric values;
• Values returned from other Excel functions or formulas.

Improduct Function Examples

The spreadsheets below show three examples of the Excel Improduct function:

Formulas:
AB
11-i=IMPRODUCT( A1, A2 )
25+10i=IMPRODUCT( "1-i", "5+10i", 2 )
3 =IMPRODUCT( COMPLEX( 5, 2 ), COMPLEX( 0, 1 ) )
Results:
AB
11-i15+5i
25+10i30+10i
3 -2+5i

Note that, in the above example spreadsheet:

• The integer 2, used in cell B2, is equal to the complex number 2+0i;
• The example in cell B3 uses the Excel Complex Function to create the complex numbers 5+2i and i.

Further details on the Excel Improduct function are provided on the Microsoft Office website.

Improduct Function Error

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

Common Errors
 #NUM! - Occurs if any of the supplied inumber arguments are not recognised as complex numbers. #VALUE! - Occurs if any of the supplied inumber arguments are logical values.