# 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:
A B
1 5+2i =IMDIV( A1, A2 )
2 1+i =IMDIV( "2+2i", "2+i" )
3   =IMDIV( "9+3i", 6 )
4   =IMDIV( COMPLEX( 5, 2 ), COMPLEX( 0, 1 ) )
Results:
A B
1 5+2i 3.5-1.5i
2 1+i 1.2+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 0 or Any of the supplied inumber arguments are not valid complex numbers. #VALUE! - Occurs if either of the supplied inumber arguments are logical values.