IMLN in ONLYOFFICE: Complex natural logarithm with Examples

=IMLN(inumber)

All arguments shown above are required; the official function page does not describe optional parameters or assumed defaults. inumber is a complex number of the form x+yi or x+yj; the suffix i/j is a lowercase complex unit. Build inputs with COMPLEX(real_num,i_num,[suffix]) rather than typing nonnumeric text into real/imaginary input cells. COMPLEX assumes i if suffix is omitted. The optional square brackets in its documentation mean optional, not literal characters.

ONLYOFFICE documents manual entry with a leading = and comma-separated arguments in its Insert functions instructions. These examples use English names and comma separators; check actual regional settings before copying the formulas into localized environments. The exact tokenized spelling of localized functions and separators has not been tested.

1. Open a new empty spreadsheet in ONLYOFFICE Spreadsheet Editor. Type the headings Scenario, Real, Imaginary, Unit, Exponent, Complex value, Result in cells A1:G1 respectively.
2. Enter the data below into A2:E11. Enter real and imaginary coefficients as numbers, not strings. In C10, enter the actual formula =PI()/2 so that row 10 is reproducible to spreadsheet precision.
3. Type =COMPLEX(B2,C2,D2) in F2 and fill down through F11. F2 is mathematically 3+4i; the exact text serialization may omit zero terms or unit coefficients.
4. Type the formula indicated below in G2 and fill it down through G11. The examples use the input suffix for notation only; native suffix propagation and output formatting remain unverified.
5. Compare results to the mathematical expectations below. A small numerical difference from a decimal approximation can come from floating-point precision, complex-number branch handling or output formatting. Do not claim that the test passed natively until somebody runs it in the target edition.

For G2, enter =IMLN(F2). Fill down to G11. Row 9 is a deliberate zero-input edge case; it is not a successful logarithm or negative-power calculation.

Expected mathematical outputs (independent calculations)

Verification method: two independent Python numeric pathways (cmath double-precision and mpmath 65-digit complex arithmetic) agreed within the declared relative/absolute tolerance for every defined example. This checks algebra, not the spreadsheet engine, its display text, exact error messages or formula parser.

The conventional principal complex logarithm separates the log-magnitude from an argument (phase angle). For nonzero z, the mathematical principal argument is in (−π, π]. ONLYOFFICE’s short reference does not expressly specify every branch-cut boundary case.

For z=a+bi, calculate magnitude sqrt(a²+b²) and mathematical angle atan2(b,a). The expected principal value has real part ln(magnitude) and imaginary part angle radians.

For z=3+4i, magnitude 5 and angle atan2(4,3)≈0.9272952180, so principal Log(z)=ln(5)+0.9272952180i.

The equations describe the mathematical operation normally associated with this function. They are not proof of native ONLYOFFICE behaviour at a branch cut or near machine-precision limits. The official vendor reference describes the function purpose and basic syntax but omits some branch/error details.

Principal-logarithm expectations follow the mathematical convention. Every advanced expression is a proposed worksheet check, not an executed result.

Use the real component of a complex logarithm to interpret a log-magnitude and its imaginary component to interpret a phase. Complex logarithms are multivalued mathematically; the guide uses the principal branch for independently calculated expectations.

Compare two ways without overstating what is tested

To inspect a complex output numerically, place =IMREAL(G2) and =IMAGINARY(G2) in blank cells. Their official real-component and imaginary-component references describe the operations. Comparing numeric components avoids making assumptions about whether the editor prints i, 1i, j, extra zeros or rounded decimals. This is a recommended future native test, not an executed verification.

Input format: A typical input such as 3+4i should be constructed with =COMPLEX(3,4,"i"). 3+4i volts, a mixed i/j string, unquoted suffix arguments and a typed formula lacking = are not shown as valid inputs by the vendor. A cell that visually looks numeric may contain text.

Domain and precision: Zero complex input has no finite complex logarithm. Negative-real inputs lie on a branch cut and must be treated carefully when transferring formulas between editors or defining signed zero.

Boundary caution: The exact native error or output string for complex zero is not documented on this function page and has not been tested. Do not infer that a logarithm identity such as Log(a×b)=Log(a)+Log(b) always holds without possible multiples of 2πi.

Troubleshooting checklist:

1. Confirm the real and imaginary components in B and C are numeric and that D contains the lowercase unit i or j.
2. Use the Insert Function window to confirm the target installation recognizes the exact English function name.
3. Check the parentheses, leading =, comma separators and argument order. Test the single-cell literal formula from the advanced table before dragging down a column.
4. If a result differs from the expected mathematical value, inspect the real and imaginary components separately and compare with a reasonable decimal tolerance.
5. For zero-input, negative-real branch-cut, fractional exponent, large-magnitude and regional settings cases, record what the actual target build does. No #NUM!, #VALUE! or other exact error is claimed without an observed native test.
6. If recalculation is stale, ONLYOFFICE documents the Calculation control on the Formula tab and F9 for workbook recalculation in its Insert Functions guide; inspect the build-specific UI before assuming identical keyboard shortcuts across systems.

The current unversioned ONLYOFFICE Docs Spreadsheet Editor Help Center lists this function and describes its syntax. This is vendor-documentation evidence, not a tested claim that every Docs server, hosted web editor, Desktop Editors version, mobile build or locale supports it. The Docs changelog and the separate Desktop Editors changelog were consulted on 2026-10-13 (UTC), but the inspected material did not establish an attributable first supported release for this function. Therefore minimum Docs/Desktop version: unknown.

Export/import and Excel or Google Sheets compatibility are not established by the ONLYOFFICE help page. Another spreadsheet’s formula behaviour, rounding, error messages or complex-number branch choice cannot serve as ONLYOFFICE execution evidence. Verify in each target application and format before migrating a workbook.

• IMLN official reference — exact documented purpose, English syntax and argument type.
• COMPLEX official reference — construct i- or j-suffixed complex values for input.
• IMREAL official reference — interpret expected real output component.
• IMAGINARY official reference — interpret expected imaginary coefficient.
• IMABS official reference — interpret magnitudes; contains its own separate documentation.
• IMARGUMENT official reference — interpret phase angles in radians.
• ONLYOFFICE function catalogue and entry instructions — category navigation and manual formula entry.
• Docs changelog and Desktop Editors changelog — independently maintained release histories.