IMSECH Function in Excel: Hyperbolic Secant of a Complex Number

IMSECH Function in Excel: Hyperbolic Secant of a Complex Number 1
⏱ 1 min readUpdated 13 October 2026

Complex numbersLevel: ExpertAvailable in: Excel 2013+

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

IMSECH returns 1/cosh(z). Complex numbers are text like 3+4i; build them with COMPLEX.

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Syntax

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

Examples

Example 1

=IMSECH(A2)

Result: -0.065294027857947+0.0752249603027732i. See the worked example table below for more cases.

IMSECH in practice

Where you will use it

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

Worked example

zFormulaResult
3+4i=IMSECH(A2)-0.065294027857947+0.0752249603027732i
1-i=IMSECH(A3)0.498337030555187+0.591083841721045i
2i=IMSECH(A4)-2.40299796172238

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

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Keep reading

Excel Functions A–ZIMREAL Function in Excel: Real PartExcel Functions A–ZLINEST Function in Excel: Full Regression StatisticsExcel Functions A–ZBETAINV Function in Excel: Inverse Beta (Older Name)
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