The natural logarithm of a complex number is calculated by the following equation:
See Wikipedia for further information on complex numbers.The Excel Imln function returns the natural logarithm of a supplied complex number.
The syntax of the function is:
where the inumber argument is the complex number that you want the natural logarithm of.
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 argument can be supplied to the Excel Imln function as any of the following:
The spreadsheets below show four examples of the Imln function:
Formulas:
 Results:

Note that, in the above example spreadsheet:
Further details and examples of the Excel Imln function are provided on the Microsoft Office website
If you get an error from the Excel Imln Function, this is likely to be one of the following:
#NUM!    Occurs if the supplied inumber argument is not recognised as a complex number. 
#VALUE!    Occurs if the supplied inumber argument is a logical value. 