The Excel IMDIV Function

Dividing Complex Numbers

The formula used to divide a complex number a+bi by a complex number c+di is: Complex Numbers are explained in detail on the Wikipedia Complex Numbers Page.

Related Function:
IMPRODUCT Function

Function Description

The Excel Imdiv function calculates the quotient of two complex numbers (i.e. divides one complex number by another).

The syntax of the function is:

IMDIV( inumber1, inumber2 )

where the inumber arguments are Complex Numbers, and you want to divide inumber1 by inumber2.

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 Imdiv 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.

Excel Imdiv Function Examples

In the spreadsheet below, the Excel Imdiv function is used find the quotient of four different pairs of complex numbers.

Formulas:
AB
15+2i=IMDIV( A1, A2 )
21+i=IMDIV( "2+2i", "2+i" )
3 =IMDIV( "9+3i", 6 )
4 =IMDIV( COMPLEX( 5, 2 ), COMPLEX( 0, 1 ) )
Results:
AB
15+2i3.5-1.5i
21+i1.2+0.4i
3 1.5+0.5i
4 2-5i

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 B4 uses the Excel Complex Function to create the complex numbers 5+2i and i.

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

Imdiv Function Errors

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

Common Errors
 #NUM! - Occurs if either:The inumber2 argument is equal to 0orAny of the supplied inumber arguments are not valid complex numbers. #VALUE! - Occurs if either of the supplied inumber arguments are logical values.