The Excel IMABS Function
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Basic Description
The Excel IMABS function Returns the absolute value (the modulus) of a complex number.
The format of the function is :
IMABS( Inumber )
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Modulus of a Complex Number
The absolute value (the modulus) of a complex number is calculated as the square root of the
sum of the squares of the real and imaginary coefficients.
i.e. the modulus of the complex number, z = a + bi is :
Further information on Complex Numbers can be found on the
Wikipedia Complex Numbers Page.
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where the Inumber argument is a Complex Number.
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 argument can be supplied to the Excel Imabs function as either:
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A simple number |
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A complex number encased in quotation marks - eg. "5+3i" |
| or |
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A reference to a cell containing a complex number or a numeric value |
| or |
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A value returned from another Excel function or formula |
These are all included in the examples below.
Examples
In the example below, the Excel Imabs function is used find the absolute value (the modulus) of different complex numbers.
The format of the function is shown in the spreadsheet on the left and the results are shown in the
spreadsheet on the right.
Formulas
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A |
B |
| 1 |
5+2i |
=IMABS( A1 ) |
| 2 |
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=IMABS( "2+2i" ) |
| 3 |
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=IMABS( 6 ) |
| 4 |
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=IMABS( "3i" ) |
| 5 |
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=IMABS( COMPLEX( 4, 1 ) ) |
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Results
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A |
B |
| 1 |
5+2i |
5.385164807 |
| 2 |
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2.828427125 |
| 3 |
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6 |
| 4 |
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3 |
| 5 |
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4.123105626 |
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Further information on the Excel Imabs function can be found on the
Microsoft Office website.
Common Errors
If you get an error from the Imabs function this is likely to be one of the following :
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#NAME?
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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
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#NUM!
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Occurs if the supplied Inumber argument is not recognised as a complex number
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