IMCONJUGATE in ONLYOFFICE: Complex Conjugates and Verified Mathematics

Return the complex conjugate of one supplied complex number, retaining its real component while changing the sign of its imaginary component. The current ONLYOFFICE vendor reference documents the English formula =IMCONJUGATE(inumber). Its function group is Engineering. It was checked on 2026-10-13 UTC. Square brackets mark optional arguments in syntax descriptions; do not type those brackets in actual formulas.

Verification boundary: Vendor documentation establishes name, purpose, syntax and described input forms. Every stated mathematical result is independently calculated using complex-number algebra; no formula was executed in ONLYOFFICE Docs or Desktop Editors. Formatting, errors, locale syntax and version-specific runtime compatibility still require native checks.

=IMCONJUGATE(inumber)

The input operands are complex numbers such as 3+4i or 2-3j, represented as complex-number text produced by COMPLEX or entered in the documented form. A numeric cell containing just a real component is not a replacement for both components without an explicit COMPLEX construction. There are no undocumented optional flags, fallback values or implicit defaults in this syntax. A formula begins with =; the examples below use English function names and commas in accordance with ONLYOFFICE’s Insert Functions instructions.

Create a new empty spreadsheet. Enter the following exact values in A1:F9: A is the scenario label, B and C the real and imaginary parts of z₁, D and E the real and imaginary parts of z₂, and F the lower-case imaginary-unit label. Put headings in row 1; enter the eight data records in rows 2–9. B:E must contain numbers, not text strings with an i/j suffix.

1. In G1 write z₁ (complex) and in H1 write z₂ (complex). Enter =COMPLEX(B2,C2,F2) in G2 and =COMPLEX(D2,E2,F2) in H2. These use ONLYOFFICE COMPLEX with the two numeric coefficients and a lowercase unit suffix.
2. Fill both G2 and H2 down through row 9. In I1, type IMCONJUGATE result. In I2, type =IMCONJUGATE(G2), and fill I2 down to I9.
3. Interpret results as mathematical complex numbers. An editor may omit a zero term or render a coefficient of one differently. This article intentionally does not claim a particular exact textual serialization. Compare real/imaginary components where appropriate with IMREAL and IMAGINARY.
4. To reproduce the examples without any reference file, retain the input table, select another blank location for advanced formulas, and change one argument at a time. None of these calculations requires screenshots, macros, external data or paid services.

Expected mathematical outputs for each row

Reproducibility check: In row 2, z₁ = 3+4i and z₂ = 1−2i. The derivation is: For z = a + bi, the conjugate is a − bi; for z = a + bj, it is a − bj. The expected output in the row-2 table is a mathematical prediction, not a screenshot or confirmed ONLYOFFICE return string. To inspect numeric components separately, use =IMREAL(I2) and =IMAGINARY(I2) in unused cells; this is a proposed native check, not an executed one.

For z = a + bi, the conjugate is a − bi; for z = a + bj, it is a − bj.

In a simple alternating-current model, a phasor 3+4j has conjugate 3−4j. Its product with its conjugate is the nonnegative real number 25. This is the algebra behind squared magnitude; do not equate that mathematical identity with a verified physical power result without the necessary units and electrical context.

If source measurements carry volts, ohms or other units, attach those units to the header labels. Complex-number cells should contain parsable complex numbers rather than strings such as 3+4i volts, which are not documented as valid formula inputs.

Enter each expression in an unused cell, with the same G:H inputs created above. The formula is shown alongside its independent, mathematical expected value; it has not been run in the ONLYOFFICE application.

Read this correctly: the expressions show compositional mathematical identities, not proof of native formula evaluation for a particular release. A single complex number has two mathematical components; comparing display strings is less robust than validating both components numerically. Decimal fractions may be rounded by the editor’s display precision.

A reproducible practical application

Suppose B2/C2 are measured phasor components (3 and 4). Build G2 using COMPLEX and compute =IMCONJUGATE(G2) to obtain the mathematical conjugate 3−4i. In a second cell enter =IMPRODUCT(G2,IMCONJUGATE(G2)), whose independently computed result is real 25. Compare this with =IMABS(G2)^2 (expected 25) as a mathematical cross-check. Record the editor’s actual results before representing this as tested software compatibility.

1. Conjugate interpreted as negation. Conjugation changes only the imaginary sign; -z changes both real and imaginary signs. First review the exact input cells and argument order; if the error persists, retain the formula and installed build number in the research record.

2. Imaginary coefficient missing. Recheck the input created with COMPLEX and its imaginary numeric cell C; a zero coefficient is mathematically unchanged. First review the exact input cells and argument order; if the error persists, retain the formula and installed build number in the research record.

3. Unexpected text style for j. Compare mathematical real and imaginary parts rather than an unverified exact output string. First review the exact input cells and argument order; if the error persists, retain the formula and installed build number in the research record.

Invalid complex syntax: 3+4k, a measurement unit embedded in a complex operand, accidental spaces, missing quotes around literal text, or uppercase I/J are not established by the documented x+yi/x+yj input form. Do not invent an ONLYOFFICE error code; test on an identified build. Try =COMPLEX(3,4,"i") to construct a clean operand, then pass its cell reference to the function.

Zero components / display conventions: 0+2i, 2i, 2j, and 0 may be formatted or simplified differently from the pedagogical display in these tables. Verify underlying mathematical components; the short vendor help page does not fully define output normalization. Do not assume a particular sign, absence of 1, zero prefix or decimal digit count in the returned text.

Wrong data types and local formula settings: When formulas show as literal text, verify that the cell is not formatted as Text and that the formula begins with =. Keep B:E numeric. If your localized editor expects translated function names or semicolons, use the built-in Function Arguments window rather than indiscriminately replacing commas. The source reference is English; cross-language parsing was not tested.

Precision, extreme operands and platform differences: Finite-precision arithmetic may make comparisons of fractional outputs approximate. The vendor article for this function does not establish a numeric tolerance, an exhaustive overflow behaviour table, an earliest supported software version or an identical web/desktop error response. Preserve the difference between mathematical undefined results, actual native #...! errors and help-documentation checks.

Diagnostic sequence when a formula fails

1. Open a new blank file, set B2=3 and C2=4 as numbers, then enter =COMPLEX(B2,C2,"i") into G2.
2. Verify B2/C2 are numeric and G2 uses the explicit lowercase "i" suffix from step 1.
3. For a two-operand function, create H2 with =COMPLEX(1,-2,"i"). For IMSUM/IMPRODUCT, start with just the first operand before adding more.
4. Enter the relevant formula from the first row of the worked table exactly. If the formula assistant shows different translated names or separators, follow its regional convention.
5. Use IMREAL and IMAGINARY for numerical component checks when supported; record exact software/host build and observed error text.
6. Do not treat independently computed values shown here as successful application test results.

According to the official Spreadsheet Editor Insert Functions guide, functions can be entered directly from the formula bar, reached from the Home/Formula tabs or selected in the Function Arguments dialog. For this family choose Formula → More functions → Engineering, or search the exact function name. That English guide says formula arguments are separated by commas. The Advanced Settings guide documents formula language and regional controls; therefore the text of a formula in a localized installation may differ. Do not assume Excel, Google Sheets or another spreadsheet program establishes ONLYOFFICE execution or translation.

Edition distinction: The primary function reference is on the current unversioned ONLYOFFICE Docs Spreadsheet Editor Help Center. Documentation listing is not proof that any particular deployed Docs web server or Desktop Editors build executes the function, nor proof that the feature existed in historical versions. Docs release history and Desktop Editors release history are separate. Neither the first-supported Docs version nor the first-supported Desktop Editors version has been verified for IMCONJUGATE; no version-compatibility table or feature parity should be inferred from the article title. For deployment-specific compatibility, test an identified web or desktop version, including localized syntax and edge-case errors.

• ONLYOFFICE IMABS reference — related complex-number operation.
• ONLYOFFICE IMREAL reference — related complex-number operation.
• ONLYOFFICE IMAGINARY reference — related complex-number operation.
• ONLYOFFICE IMPRODUCT reference — related complex-number operation.
• ONLYOFFICE Insert Functions and current Engineering function list — formula UI and help-catalogue entry.
• ONLYOFFICE Advanced Settings — regional and function-language settings.
• ONLYOFFICE Docs changelog — separate web/server release history; does not independently date this function.
• ONLYOFFICE Desktop Editors changelog — separate desktop release history, not evidence of first support.

Verification: Official syntax and inputs were checked against the linked vendor references. All table and advanced examples were independently calculated with exact complex arithmetic. Native ONLYOFFICE Docs and Desktop execution was not performed. Error messages, output serialization and localized or historical compatibility remain unverified.