Related Function:

The IMLN function returns the natural logarithm of a complex number in x + yi or x + yj text format.

Syntax

=IMLN(inumber)

Arguments

Argument Description
inumber A complex number for which you want the natural logarithm. The inumber argument can be supplied to the IMLN function as either:

  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 function or formula

Note: Use the COMPLEX function to convert real and imaginary coefficients into a complex number.

Examples

  A B C D
1 Data Formula Result Notes
2 2.5-i =IMLN(A2) 0.990500734433292-0.380506377112365i Natural logarithm of 2.5-i
3   =IMLN(2) 0.693147180559945  
4   =IMLN(“3+4i”) 1.6094379124341+0.927295218001612i  
5   =IMLN(COMPLEX(1,-1)) 0.346573590279973-0.785398163397448i  

Common Function Error(s)

Problem What went wrong
#NUM! Occurs if the supplied inumber argument is not recognized as a complex number
#NAME? Occurs when Analysis ToolPak add-in is not enabled

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

    \[ \label{eq:imexp}ln(x+yi)=ln\sqrt{(x^2+y^2)}+itan^{-1}\left(\frac{y}{x}\right)\]

Further information on Complex Numbers can be found on the Wikipedia Complex Numbers Page.