IMARGUMENT Function in Excel: Angle of a Complex Number

IMARGUMENT Function in Excel: Angle 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. IMARGUMENT in practice
  5. Where you will use it
  6. Worked example
  7. Mistakes people make
  8. Related functions

IMARGUMENT returns the angle θ in radians (phase angle). Complex numbers are text like 3+4i; build them with COMPLEX.

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Syntax

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

Examples

Example 1

=IMARGUMENT(A2)

Result: 0.927295218. See the worked example table below for more cases.

IMARGUMENT in practice

Where you will use it

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

Worked example

zFormulaResult
3+4i=IMARGUMENT(A2)0.927295218
1-i=IMARGUMENT(A3)-0.785398163
2i=IMARGUMENT(A4)1.570796327

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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