The IMLN function returns the natural logarithm of a complex number in x + yi or x + yj text format
Syntax:= IMLN(inumber)
The IMLN function syntax has the following arguments:
 Inumber: Required. A complex number for which you want the natural logarithm
Example: Let’s look at some Excel IMLN function examples and explore how to use the IMLN function as a worksheet function in Microsoft Excel:
Syntax: =IMLN(A2)
Result:
Based on the Excel spreadsheet above, the following IMLN examples would return:
Syntax: =IMLN(A3)
Result: 1.03972077083992+0.785398163397448i
Syntax: =IMLN(A4)
Result: 1.6094379124341+0.927295218001612i
Syntax: =IMLN(A5)
Result: 0.346573590279973+0.785398163397448i
Syntax: =IMLN(A62)
Result: 1.38629436111989
Syntax: =IMLN(A7)
Result: 3.17805383034795+1.5707963267949i
Syntax: =IMLN(A8)
Result: 2.24990483516513+0.321750554396642i
Syntax: =IMLN(A9)
Result: 1.85678603335215+0.896055384571344i
Syntax: =IMLN(A10)
Result: 2.528122902674151.07144960511477i
Syntax: =IMLN(A11)
Result: 2.564949357461541.17600520709514i
Syntax: =IMLN(A12)
Result: 3.10730404921111.10714871779409j
Syntax: =IMLN(A13)
Result: 5.48520997886308+1.47525476601799i
Note:
 Use COMPLEX to convert real and imaginary coefficients into a complex number.

The natural logarithm of a complex number is: