The Excel IMLN Function

Related Function:
IMEXP Function
Natural Logarithm of a Complex Number

The natural logarithm of a complex number is calculated by the following equation :

Equation for the Natural Logarithm of a Complex Number

See Wikipedia for more information on complex numbers.

Basic Description

The Excel Imln function returns the natural logarithm of a supplied complex number.

The format of the function is:

IMLN( inumber )

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 Imln function as either:

  or  or  or

These are all included in the examples below.

Imln Function Examples

The spreadsheet below shows 4 different examples of the Imln function.

Examples of use of the Excel Imln Function
Excel Imln Function Results

Note that, in cell B1 of the above spreadsheet, the supplied inumber argument is the integer 2, which is equal to the complex number 2+0i.

Further information and examples of the Excel Imln function can be found on the Microsoft Office website

Imln Function Errors

If you get an error from the Excel Imln 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

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.

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