IMLOG10 Function (Gnumeric)

IMLOG10(z) returns the principal base-10 logarithm of a complex number. Mathematically it is ln(z) / ln(10), with real part log₁₀(|z|) and imaginary part Arg(z)/ln(10). =IMLOG10("3+4i") has independently calculated expectation 0.6989700043+0.4027191963i, not log₁₀(3) or log₁₀(4) separately. Official Gnumeric Complex manual, checked 2026-10-13.

=IMLOG10(z)

z (required): one valid complex number, such as "3+4i", a reference to its cell, or a value built by COMPLEX. No optional arguments or defaults are documented. The base is always 10; it is not a second parameter. The function is different from real-number LOG10, which does not express the angle of a non-real argument. Gnumeric manual, checked 2026-10-13.

The examples are independent mathematical reference values rounded to ten decimal places; they do not assert exact output strings from a Gnumeric executable.

For complex A2, =IMREAL(IMLOG10(A2)) is mathematically log₁₀(|A2|) and =IMAGINARY(IMLOG10(A2)) is the phase (radians) scaled by 1/ln(10). To calculate a magnitude-only 20-log decibel expression for an amplitude ratio, use =20*LOG10(IMABS(A2)) (independent arithmetic expectation for 3+4i: 20*log₁₀(5) ≈ 13.9794000867). That is a different quantity from 20 multiplied by the full complex logarithm. For power ratios, the conventional factor is 10, not 20; verify the physical meaning and units before interpreting a measurement.

If comparing bases, IMLOG10(z) * ln(10) = IMLN(z) mathematically on the same branch. A numeric check using IMREAL, IMAGINARY and LN(10) is safer than a raw string comparison or assuming an application returns native complex numeric objects.

Related pages: IMLN, IMLOG2, IMARGUMENT, and IMABS. Gnumeric manual, checked 2026-10-13.

Boundary conditions: A complex logarithm at zero is mathematically undefined; a zero-magnitude input needs a defined error-handling policy. The principal phase has a branch cut along the negative real axis, so a phase plot can jump by nearly 2π even for smooth underlying data. Format precision and exact error tokens require native validation.

Create a blank Gnumeric sheet. Enter these complex-number text literals without a leading = in column A. Use plain English-formatted samples with a period as decimal separator; inspect your locale’s input conventions before adapting them.

Enter the article’s function formula in D2 and copy to rows 3–5 if desired. For a constructed input, enter =COMPLEX(B2,C2) in D7 and use the article’s function around D7. COMPLEX’s manual signature is COMPLEX(x,y,i) with the suffix defaulting to i. The comma shown follows the English-language Gnumeric manual; locales may change separators and decimal conventions. This article does not claim to have tested other locale syntaxes. Sources: COMPLEX documentation; locale documentation (checked 2026-10-13).

• Unparseable text: The online Gnumeric 1.12 manual says #VALUE! for invalid complex input. The checksum-verified official 1.12.62 source returns #NUM! for malformed complex strings; other unsupported value types may yield #VALUE!. This resolves the release-source provenance question, but is not a native execution result.
• Quoted numeric-looking strings: Ensure your input contains a valid complex representation ("3+4i" or "2-1i"), not a stray unit, spreadsheet formula, or text with thousands separators. The i/j convention belongs inside the complex text; do not append it to an ordinary LN/LOG result.
• Locale/import: Formula syntax and text parsing can vary with decimal separators. The one-argument function signature stays one argument, but nested COMPLEX(B2,C2) uses a delimiter that your localized installation may represent differently. Test an imported worksheet rather than silently replacing commas with semicolons; consult Gnumeric locale documentation.
• Precision and formatting: Calculated complex results are floating-point approximations; displayed digits, placement of i or j, and very small residual coefficients can vary. For verification compare real and imaginary components numerically (e.g. IMREAL/IMAGINARY) rather than comparing raw strings.
• Compatibility: The manual marks this function Excel compatible, but this is Gnumeric’s documented classification. It does not establish identical parsing, error codes, version support, formatting, or calculations in another spreadsheet. Confirm a workbook separately in each target product.
• Testing boundary: All expected values on this page were independently derived using Python’s standard cmath/math modules and analytic identities. Native Gnumeric checks: 0. Errors described as unresolved are deliberately not disguised as tested results.

1. Gnumeric Complex manual — signature, purpose, input note, compatibility and principal branch where stated.
2. Official function catalogue — IMLOG10: Complete / Exhaustive (upstream catalogue status, not observed execution).
3. Gnumeric 1.12.62 release announcement — general complex-function compatibility improvements, not a claim of per-example native testing.
4. Official Gnumeric 1.12.62 source archive — inspected complex callbacks and shared parser in plugins/fn-complex/functions.c; release archive checked against its official SHA-256 checksum.
5. Gnumeric download policy and locale documentation — platform availability and locale caveats.

Native validation remains outstanding: exact displayed results, error cells, locale behavior and workbook round-trips have not been checked in a running Gnumeric installation.