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The Excel IMDIV Function
Dividing Complex Numbers
When dividing complex numbers a+bi by complex number c+di, the formula used is as follows:
Further information on Complex Numbers can be found on the Wikipedia Complex Numbers Page.
Basic Description
The Excel IMDIV function calculates the quotient of two complex numbers (ie. divides one complex number by another).
The format of the function is :
IMDIV( inumber1, inumber2 )
where the inumber arguments are both Complex Numbers, and you want to divide inumber1 by inumber2.
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 builtin 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:
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.
Excel Imdiv Function Examples
In the example below, the Excel Imdiv function is used find the difference between 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  32i 

2  1+i  1.2+0.4i 

3   1.5+0.5i 

4   25i 


Further information on the Excel Imdiv function can be found on the Microsoft Office website.
Imdiv Function Common 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 the supplied inumber argument is not recognised as a complex number 
#NAME?    Occurs when Analysis ToolPak addin is not enabled in your Excel. You will need to enable the addin if you want to use the Excel complex number functions.
+ Show How to Do This in Excel 2003:
 From the Tools dropdown menu, select the option AddIns ...
 An 'AddIns' window will pop up. From this, select the option Analysis ToolPak and click OK
+ Show How 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 AddIns
 In the 'Manage:' box, select Excel Addins and click Go...
 An 'AddIns' window will pop up. From this, select the option Analysis ToolPak and click OK
+ Show How to Do This in Excel 2010 or Excel 2013:
 Click the File tab (top left of your spreadsheet) and select Options
 From the menu on the left hand side, select AddIns
 If the window that pops up doesn't show the 'Addins' list, use the 'Manage:'
dropdown menu (at the bottom of the window) to select Excel Addins. Click Go...
 From the 'AddIns' window, select the option Analysis ToolPak and click OK
