IMLN Function in Excel: Natural Log of a Complex Number

IMLN Function in Excel: Natural Log of a Complex Number 1
⏱ 1 min readUpdated 5 October 2026

Complex numbersLevel: ExpertAvailable in: Excel 2007+

In this article
  1. Syntax
  2. Examples
  3. Example 1
  4. IMLN in practice
  5. Where you will use it
  6. Worked example
  7. Mistakes people make
  8. Related functions

IMLN returns ln(z). Complex numbers are text like 3+4i; build them with COMPLEX.

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Syntax

=IMLN(inumber)
Argument What it means
inumber Complex number as text, e.g. “3+4i”

Examples

Example 1

=IMLN(A2)

Result: 1.6094379124341+0.927295218001612i. See the worked example table below for more cases.

IMLN in practice

Where you will use it

  • AC circuit calculations (impedance, phase)
  • Signal processing
  • Engineering coursework

Worked example

zFormulaResult
3+4i=IMLN(A2)1.6094379124341+0.927295218001612i
1-i=IMLN(A3)0.346573590279973-0.785398163397448i
2i=IMLN(A4)0.693147180559945+1.5707963267949i

Results calculated in Excel.

Mistakes people make

MistakeWhat to do instead
Spaces inside the text"3 + 4i" gives #NUM!; write 3+4i
Result is textUse IMREAL/IMAGINARY to get numbers back

COMPLEX · IMABS · IMREAL

📚 Part of the free Excel course: Beginner → Expert · Try it in the Formula Lab or ask the AI Helper.

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