IMARGUMENT Function in ONLYOFFICE Spreadsheet Editor: Complex Angles

• Introduced: The original introduction version and date are not established by the official sources checked.
• Availability: Documented in the current ONLYOFFICE Spreadsheet Editor help; no final working-version endpoint is established.
• Scope: Docs and Desktop Editors release separately. This unversioned help does not establish availability in every older build, mobile client or deployment.
• Checked: October 14, 2026, against the official function reference. Documentation check; not a new native test.

Return an angular argument θ for the specified complex value, expressed in radians, rather than the magnitude or a component. Its exact current English-reference syntax is =IMARGUMENT(inumber). This is documented in the official ONLYOFFICE IMARGUMENT function reference, checked 2026-10-13 UTC. Any square brackets in the syntax indicate an optional argument; they are not characters to enter in your formula.

Evidence boundary: Vendor claim checks cover purpose/arguments/current documentation; sample results are separately computed mathematical predictions and were not observed in ONLYOFFICE.

=IMARGUMENT(inumber)

Argument rule: One required input; no optional argument or default is documented. Numbers with an imaginary unit should use lowercase i or j as specified by the vendor; direct literal coercion beyond the documented notation is not guaranteed. Do not confuse English argument separators with decimal separators.

In a new worksheet, type the following records. The numbers in B and C must be numeric cells; D contains a lowercase text suffix (i or j). Type the headers into row 1 and the data into rows 2–9. Leave columns E onward empty until entering the formulas. This dataset is original teaching data and does not depend on a downloaded example file.

Select E2 (outside the input table) and enter =COMPLEX(B2,C2,D2). Fill E2 down through E9. This uses the documented three-argument form and lets every later example read the same complex-number cells. If the calculated text contains a simplified zero term, compare the mathematical number rather than presuming a precise string-rendering convention—the official function pages do not specify all serialization cases. Do not paste explanatory table labels into numeric fields.

With column E containing the COMPLEX formula from the practice table, type =IMARGUMENT(E2) into F2 and fill only across the nonzero rows you intend to test. The mathematics of a complex angle is based on the two-argument arctangent atan2(imaginary component, real component); its sign and quadrant matter. The vendor confirms the output is an angle in radians but the brief public article does not spell out every principal-branch, axis-boundary or signed-zero convention. The table below uses the conventional mathematical principal argument as an independently calculated expectation, not a proved ONLYOFFICE branch implementation.

In G2 enter =DEGREES(F2); the official DEGREES article documents that it converts radians to degrees. For row 2, the independent expected value is approximately 53.1301023542. Rounding cell display to two decimals should show about 53.13, although the underlying number is not exactly 53.13.

Why an ordinary one-argument arctangent is unsafe

The quotient y/x loses quadrant information. For the second data row, x = −5 and y = +12, so atan(y/x) alone produces a negative acute angle even though the vector is in the second quadrant. The mathematically correct principal direction is approximately 112.62°. We rely on an independent two-argument atan2(y,x) calculation for expectations and do not claim ONLYOFFICE’s spreadsheet ATAN2 function has the same argument order as a programming-language atan2 call.

Advanced example: polar representation

For E2=3+4i, combine =IMABS(E2) and =IMARGUMENT(E2) to obtain the independent polar values radius 5 and angle about 0.927295218002 radians. From these, the mathematical reconstruction is x = 5×cos(θ) ≈ 3, y = 5×sin(θ) ≈ 4. This is a mathematical consistency check, not an observed native round-trip result.

In engineering, phase direction and amplitude answer different questions. Use the linked vendor IMABS reference for magnitude, IMREAL for x and IMAGINARY for y.

• Exactly zero complex number: the mathematical phase is undefined because every angle describes the origin. Row 7 is therefore deliberately excluded from the numeric angle table. The checked vendor page does not specify whether ONLYOFFICE returns a specific error, value, or other behaviour; native testing is required before presenting a result.
• Negative real axis: mathematically +π and −π describe the same direction. A principal-branch convention must be chosen for an exact signed result; the checked vendor article does not state that boundary convention. Do not claim an exact negative-axis output without native execution.
• Other axes/quadrants: calculate signs from both components; negative imaginary values usually give negative principal angles, but branch treatment should be checked in the actual editor.
• Degrees vs radians: multiplying the angle by 180/π or wrapping it in DEGREES changes units, not the complex value. A common mistake is reading 0.927 as 0.927 degrees.
• Malformed text or absent argument: IMARGUMENT requires one inumber with complex notation; the article gives no exhaustive specific-error lookup. Record any actual displayed error instead of inventing one.
• Numerical precision: do not compare long floating-point results as strings; show appropriate decimal places and document tolerances. At very large inputs, floating-point behaviour is build-dependent and untested here.

If results disagree, start with =IMARGUMENT(COMPLEX(3,4)), then =DEGREES(IMARGUMENT(COMPLEX(3,4))). Check the input signs, radians-versus-degrees display, and whether your formula language changes separators. Only after these controls should you try boundary cases or an imported complex literal.

In the current ONLYOFFICE Spreadsheet Editor Help Center, these functions appear in the Engineering group. To locate them, use Formula → More functions → Engineering, or the Insert Function dialog and search for the exact English name. You can also type formulas directly, starting with =. This navigation and keyboard entry method are documented by the official Insert Functions guide (checked 2026-10-13).

All formulas here use the official English names and comma-delimited syntax. The ONLYOFFICE Advanced Settings reference explains that formula language and regional settings can vary. If your editor displays a translated function name or expects another list separator, use its formula assistant rather than blindly substituting punctuation. Decimal commas and argument separators are separate regional concerns. In example formulas, literal complex numbers and the suffix are text in double quotes; unquoted entries such as 3+4i are not equivalent to a quoted text literal.

Edition and version applicability

The current unversioned ONLYOFFICE Docs Help Center documents this function. That verifies present official documentation, not a first-supported version, successful execution in every deployed Docs server, or equivalent outcomes in all versions of Desktop Editors. The ONLYOFFICE Docs changelog and Desktop Editors changelog were consulted on 2026-10-13; neither was used to infer an undocumented first introduction release for this function. Native tests on identified Docs/web and Desktop versions are still required, especially for edge-case parsing, exact error text, and round-trip formatting. Excel, Google Sheets, other spreadsheet products and cmath are not evidence of ONLYOFFICE’s native behaviour.

Verification: Argument definitions and purposes come from the linked official references. Expected values were independently calculated. Native ONLYOFFICE Docs web or Desktop execution, historical-edition testing, localized syntax, exact errors and output formatting were not tested.

• ONLYOFFICE IMARGUMENT function: primary syntax and purpose.
• ONLYOFFICE Insert Functions: engineering category and how to enter formulas.
• ONLYOFFICE Spreadsheet Editor Advanced Settings: formula language and region.
• ONLYOFFICE Docs changelog: product release history, not proof of this function’s introduction.
• ONLYOFFICE Desktop Editors changelog: independent desktop release history.
• Related official references: COMPLEX, IMREAL, IMAGINARY, IMABS.