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COMPLEX Function (LibreOffice Calc)

Engineering Beginner LibreOffice Calc Introduction not established

The COMPLEX function converts real and imaginary numeric components into a complex number formatted as text. It is used in engineering, signal processing, AC circuit analysis, and any workflow involving complex arithmetic.

Verification status: Consult the documentation, examples and any stated test scope below. How formula examples are checked

Availability and version history

  • Introduced: Documented by LibreOffice 26.8.1.1; original introduction not established.
  • Availability: Supported in LibreOffice 26.8.1.1, verified against its function registry. This identifies a supported release, not a final working version.
  • Scope: Desktop Calc, using the English function name. Availability in other spreadsheet applications is separate.
  • Checked: 2026-10-14 — function reference; versioned support. Documentation/source check; not a new native test. Existing example-specific test claims below retain their stated scope.
The **COMPLEX** function converts real and imaginary numeric values into a **complex number string** in the form `"a+bi"` or `"a+bj"`. It is widely used in engineering, AC circuit analysis, and mathematical modeling.

What the COMPLEX Function Does

  • Combines real and imaginary parts into a complex number
  • Supports "i" or "j" notation
  • Returns a text string, not a numeric type
  • Works seamlessly with other IM* complex functions

Syntax

COMPLEX(real; imaginary; [suffix])

Arguments

  • real:
    The real component of the complex number.

  • imaginary:
    The imaginary component.

  • suffix (optional):
    "i" (default) or "j" — engineering notation.

Basic Examples

Default imaginary unit (i)

=COMPLEX(3; 4)
→ "3+4i"

Using engineering notation (j)

=COMPLEX(5; -2; "j")
→ "5-2j"

Zero imaginary part

=COMPLEX(7; 0)
→ "7+0i"

Zero real part

=COMPLEX(0; 9)
→ "0+9i"

Advanced Examples

Build a complex impedance

=COMPLEX(10; 5)
→ "10+5i"

Combine with IMSUM

=IMSUM(COMPLEX(3;4); COMPLEX(1;-2))
→ "4+2i"

Use with IMABS to compute magnitude

=IMABS(COMPLEX(A1; B1))

Use with IMSQRT for square roots of negative numbers

=IMSQRT(COMPLEX(-4; 0))

Generate a phasor from magnitude and angle

=COMPLEX(R*COSH(θ); R*SINH(θ))

Build a dynamic complex expression

=COMPLEX(A1; A2 * PI())

Edge Cases and Behavior Details

COMPLEX returns a text string, not a numeric complex type

All IM* functions accept this string format.

Behavior details

  • Imaginary part sign is handled automatically
  • "i" or "j" must be lowercase
  • Non-numeric inputs → Err:502
  • Suffix must be "i" or "j" only
  • COMPLEX does not validate magnitude or angle

COMPLEX of an error → error propagates

Common Errors and Fixes

Err:502 — Invalid argument

Cause:

  • Non-numeric real or imaginary part
  • Invalid suffix (anything other than “i” or “j”)

Fix:

  • Validate numeric inputs
  • Use only “i” or “j”

Unexpected formatting

Cause:

  • Imaginary part negative → auto‑formatted as subtraction

Fix:

  • This is expected behavior

Best Practices

  • Use COMPLEX to construct valid inputs for IM* functions
  • Use "j" for electrical engineering workflows
  • Keep real and imaginary parts in separate cells for clarity
  • Use IMABS, IMARG, IMSUM, IMDIV, etc., for further operations
  • Avoid mixing COMPLEX strings with numeric arithmetic
COMPLEX is the gateway to Calc’s entire complex‑number ecosystem — once you construct the number, every IM* function becomes available.
  • IMREAL / IMAG — extract components
  • IMABS — magnitude
  • IMARG — phase angle
  • IMCONJUGATE — conjugate
  • IMSUM / IMPRODUCT / IMDIV — arithmetic
  • IMSQRT — square root of complex numbers

By mastering COMPLEX, you can build powerful engineering, signal‑processing, and mathematical models in LibreOffice Calc.

Reproducible example (tested in LibreOffice Calc)

This standalone example was calculated in LibreOffice Calc 25.2.3.2 and matched the expected value. It is a practical cross-check of one usage, not proof that every example elsewhere on this page is correct.

=COMPLEX(3;4)

Expected result: 3+4i.

Combine real and imaginary components into a complex number.

If the result differs, check the referenced cells, argument separators and number formatting. For more information, consult the LibreOffice Calc official help.