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 further information on complex numbers.

Function Description

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

The syntax of the function is:

IMLN( inumber )

where the inumber argument is the complex number that you want the natural logarithm of.

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 argument can be supplied to the Excel Imln function as any of the following:

  • A simple number;
  • A complex number encased in quotation marks - e.g. "5+3i";
  • A reference to a cell containing a complex number or a numeric value;
  • A value returned from another Excel function or formula.

Imln Function Examples

The spreadsheets below show four examples of the Imln function:

  A B
1   =IMLN( 2 )
2   =IMLN( "1-2i" )
3 2.5-i =IMLN( A3 )
4   =IMLN( COMPLEX( 1, -1 ) )
  A B
1   0.693147180559945
2   0.80471895621705-1.10714871779409i
3 2.5-i 0.990500734433292-0.380506377112365i
4   0.346573590279973-0.785398163397448i

Note that, in the above example spreadsheet:

Further details and examples of the Excel Imln function are provided 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.
#VALUE! - Occurs if the supplied inumber argument is a logical value.