IMCONJUGATE in Zoho Sheet: Examples and a Documentation Caveat

IMCONJUGATE is documented to return the complex conjugate as text: the real coefficient stays the same and the imaginary coefficient changes sign. Zoho’s example =IMCONJUGATE("2+3j") gives 2−3j, and its =IMCONJUGATE("5j") example gives −5j.

However, the same official page prints =IMCONJUGATE("1+4i") with the unchanged result 1+4i, contradicting its stated definition. The mathematical conjugate is 1−4i. That documentation inconsistency remains unresolved here; it is not evidence of a confirmed calculation-engine defect, and this guide does not certify the function’s runtime behavior for that i-form input.

=IMCONJUGATE(complex_number)

The official IMCONJUGATE reference describes the argument as text representing a complex number. Quote a literal such as "2+3j", or reference a cell containing the text. A naked expression 2+3j is not a quoted complex-number string.

The examples in this guide distinguish a mathematical value from its exact display. A real result might be written mathematically as 7 or 7+0j, but these sources do not establish which string a particular runtime would return. Do not use an assumed punctuation or zero-suppression format as a numerical verification.

Put the text 2+3j in A2 and enter:

=IMCONJUGATE(A2)

Its literal equivalent is =IMCONJUGATE("2+3j"). The documented example and independent arithmetic agree: the real coefficient remains 2, while the imaginary coefficient changes from 3 to −3.

Conjugation is not negation of the entire number. Negating 2+3j gives −2−3j; conjugating it gives 2−3j. It is also not the magnitude: the magnitude is the nonnegative real number √13, approximately 3.6055512755.

On an ordinary complex plane, this mathematical transformation reflects the point across the real axis. The vertical coordinate changes sign while the horizontal coordinate stays fixed.

The following values are independently derived conjugates, with exact coefficients. Apart from the two explicitly identified vendor j examples, they are not asserted Zoho execution results.

A negative imaginary coefficient becomes positive. A purely real value is unchanged mathematically. The final row is deliberately a conflict check: its coefficients follow the conjugate definition, while the page’s example text does not. It must not be presented as a successful application test.

The mathematical product of 2+3j and its conjugate is:

(2+3j)(2−3j) = 4−6j+6j−9j² = 13

The imaginary terms cancel and j²=−1. In general, multiplying a + bj by its conjugate gives a²+b², a nonnegative real value. Applying conjugation twice also returns the original number mathematically. These are useful independent identities for reasoning about results, not evidence that every composed spreadsheet formula was run.

For a worked division, multiply the numerator and denominator of (1+j)/(2+3j) by 2−3j. The numerator becomes 5−j and the denominator becomes 13, giving the exact mathematical result 5/13−(1/13)j. This explains why conjugation appears in complex division; it does not convert a complex number into an ordinary real spreadsheet number.

IMPRODUCT and IMDIV are related operations. IMREAL and IMAGINARY address coefficients, while IMABS addresses magnitude. COMPLEX constructs a representation from coefficients. Keep these different purposes separate when interpreting a worksheet.

The short help supplies generic error descriptions rather than a complete complex-string parser contract. Exact outcomes for malformed strings, whitespace, uppercase suffixes, mixed suffixes or unexpected types have not been established here. The page’s explicit i-form contradiction is a reason to verify the intended suffix and coefficients in the actual target workbook before relying on that case.

An erroneous static table cannot prove an engine bug. The sources support the mathematical definition and the displayed j examples, with the unresolved inconsistency stated above.

Official documentation was checked on October 18, 2026. No authored Zoho workbook or calculation-engine execution was performed; the numerical work here is independent complex arithmetic. Exact runtime text formatting, mobile/import parity and the conflicting i example remain unverified. The rolling page does not identify the function’s first release or establish retirement/deprecation history.