IMCOSH Function in Excel: Hyperbolic Cosine of a Complex Number

IMCOSH Function in Excel: Hyperbolic Cosine of a Complex Number 1
⏱ 1 min readUpdated 5 October 2026

Complex numbersLevel: ExpertAvailable in: Excel 2013+

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

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

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Syntax

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

Examples

Example 1

=IMCOSH(A2)

Result: -6.58066304055116-7.58155274274654i. See the worked example table below for more cases.

IMCOSH in practice

Where you will use it

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

Worked example

zFormulaResult
3+4i=IMCOSH(A2)-6.58066304055116-7.58155274274654i
1-i=IMCOSH(A3)0.833730025131149-0.988897705762865i
2i=IMCOSH(A4)-0.416146836547142

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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