IMCONJUGATE in WPS Spreadsheet: Reverse the Imaginary Sign
Find a complex conjugate in WPS Spreadsheet, retaining the real component and reversing the imaginary component with independent examples.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =IMCONJUGATE("3+4i") represents 3−4i. The real part stays 3, while the imaginary coefficient changes from 4 to −4.
Syntax and operation
=IMCONJUGATE(inumber)
The required argument is complex text. The official formula image defines the conjugate of x+yi as x−yi. This is reflection across the real axis. It is not negation of the whole number: the negative of 3+4i would be −3−4i, which changes both coefficients.
No branch selection or angle unwrapping is involved in conjugation. The operation is defined directly by the two coefficients. The mathematical value of a double conjugate equals the original number.
Worked example: reflect a set of points
Enter the following complex text in A2:A5 and put =IMCONJUGATE(A2) in B2. Copy the reference down.
| Cell | Input text | Expected mathematical conjugate |
|---|---|---|
| A2 | 3+4i | 3−4i |
| A3 | -3+4i | −3−4i |
| A4 | 1+2i | 1−2i |
| A5 | 0+0i | 0 |
The table expresses complex values, not a promise of exact WPS string serialization. In particular, a zero imaginary component may be formatted differently from the notation used to explain the mathematics. Compare the real and imaginary coefficients, not an assumed decimal string length or zero suffix.
For A3, the real component is already negative. Conjugation leaves it at −3 and reverses only the +4i part. This control helps catch a mistaken “change every sign” interpretation.
Advanced use: check a magnitude identity
Take z=3+4i and its conjugate 3−4i. Multiplication gives 9−12i+12i−16i²=25, because i²=−1. The imaginary terms cancel, leaving the squared magnitude. This independent identity is useful for checking a manually calculated result: a wrong sign in the conjugate would generally spoil the cancellation.
The same input and its conjugate have equal magnitude, 5, although their positions in the complex plane differ. A table of magnitudes alone cannot distinguish them. Keep the original input alongside the conjugate when the sign of the imaginary coefficient carries meaning.
For a purely real mathematical value, conjugation leaves the value unchanged. The worked zero case is the simplest such control; it does not establish all alternative parser spellings for real-only inputs. The examples deliberately use explicit complex text rather than depending on implicit conversion of a numeric cell.
Text and arithmetic are separate concerns
The conjugate is a complex representation, not a scalar negative number. Avoid feeding its displayed text into ordinary arithmetic without checking that the receiving function accepts complex text. A visual minus sign in the result belongs to the imaginary coefficient and should not be interpreted as a negative magnitude.
The official lesson also describes using COMPLEX to construct representations from coefficients, but the examples here do not require its optional arguments or suffix rules. They can be reproduced directly with the quoted text shown.
Input handling and output checks
Pass a well-formed complex text value, such as "3+4i", or a cell containing that text. The WPS lesson describes x+yi and x+yj notation. These examples consistently use i; the imaginary unit is not a cell name or an unquoted variable. A cell reference supplies the stored complex text, whereas a quoted literal supplies the text directly.
The cited lesson does not provide a complete error or parsing table. Whitespace, uppercase suffixes, malformed expressions, locale-specific decimal punctuation, blank cells, logical values and array arguments are therefore outside the asserted examples. No Excel-derived error code or coercion rule is substituted for those gaps. Keep coefficients small when checking the examples; overflow and underflow behavior for extreme values is not established.
Evidence and version scope
The official WPS Academy IMCONJUGATE lesson, published 2019-06-19, explicitly applies to WPS Office for Windows Personal. It was reviewed on October 18, 2026. The numeric build, introduction release and last supported version remain unknown. The source does not identify this function as deprecated or retired. Support in Linux, other editions and other platforms is not established by this lesson.
The worked examples are original mathematical expectations based on the official contract and formula illustration. They were not executed in WPS. Historical vendor demonstrations are documentation, not our application tests; no screenshot or runtime precision guarantee is supplied. English names and comma separators follow the lesson. Localized entry, workbook interchange and exact output formatting require verification in the intended client.