IMCONJUGATE Function (Gnumeric)

• Introduced: Documented by 1.12.62; original introduction not established.
• Availability: Supported in Gnumeric 1.12.62, based on the function-specific registration.
• Scope: Desktop; the fn-complex function module must be included and enabled.
• Checked: October 14, 2026. Documentation/source check; no new native test in Gnumeric 1.12.62.

=IMCONJUGATE(z)

There is exactly one documented input. IMCONJUGATE is not the same as negation: -(3+4i)=-3-4i, while the conjugate is 3-4i. Nor does conjugation mean taking an absolute value. Gnumeric’s reference states that an invalid complex input yields #VALUE! and identifies the function as Excel compatible [1].

Create the following small table:

Mathematically expected D2 = 3-4i, D3 = 3+4j. The exact appearance of the complex string, including whether a suffix is preserved in every code path, must be confirmed in an installed Gnumeric release; this review did not capture native outputs. All argument names and documented invalid-value error come from the Gnumeric 1.12 manual [1].

More expected expressions

The last error prediction relies on an explicit manual rule, while all other values are independent mathematical expectations, not executed application output.

Suppose an impedance estimate has real component 8 and imaginary component 6. Put 8 in A2, 6 in B2, =COMPLEX(A2,B2,"j") in C2 and =IMCONJUGATE(C2) in D2. The two complex quantities are 8+6j and 8-6j mathematically; both have modulus √(8²+6²)=10. Use =IMABS(C2) and =IMABS(D2) to check that the magnitudes match, even though the imaginary signs differ. This is a mathematical model illustrating complex conjugation; it is not a substitute for circuit-specific physical assumptions.

For z=a+bi, the identity z × conjugate(z)=a²+b² yields a nonnegative real number. With z=3+4i, the product is (3+4i)(3-4i)=9+16=25 (because the imaginary cross terms cancel and i²=-1). In a Gnumeric worksheet with A2=3, B2=4:

C2: =COMPLEX(A2,B2)
D2: =IMCONJUGATE(C2)
E2: =IMREAL(IMPRODUCT(C2,D2))
F2: =A2^2+B2^2
G2: =IMABS(C2)^2

Expected E2=F2=G2=25. A useful additional check is =IMAGINARY(IMPRODUCT(C2,D2)), whose mathematically expected value is 0. If real and imaginary parts are mixed up, or if one term’s sign was typed incorrectly, comparing the multiple independently derived values helps flag the issue. These are proposed native checks, not tests already run; Gnumeric separately documents COMPLEX, IMPRODUCT, IMREAL, IMAGINARY, and IMABS [1].

Two further algebraic checks

Conjugation is an involution: conj(conj(z))=z. It also distributes over a sum: conj(z1+z2)=conj(z1)+conj(z2). For z1=3+4i, z2=1-2i, the sum is 4+2i and its conjugate is 4-2i. One can compare the documented function compositions =IMCONJUGATE(IMSUM("3+4i","1-2i")) and =IMSUM(IMCONJUGATE("3+4i"),IMCONJUGATE("1-2i")). Both mathematically represent 4-2i. This gives a stronger audit than assuming the first output must be correct.

The official Gnumeric 1.12 reference calls IMCONJUGATE Excel compatible [1], and the public function catalogue lists it as Complete / Basic [2]. Neither is evidence of identical result strings in all Excel builds, nor of native execution in Gnumeric here. Gnumeric 1.12.62’s announcement reports complex-function compatibility improvements [3]. Application-level validation should exercise negative/positive/purely imaginary numbers, both suffixes, conjugate-of-conjugate, multiplication-by-conjugate, malformed inputs, zeros and XLSX import/export on a current Gnumeric installation. The official download page says Linux/BSD distribution packages are preferred and Windows binaries are not currently distributed by the project [4].

• COMPLEX — build the starting number.
• IMREAL — verify unchanged real part.
• IMAGINARY — verify reversed imaginary sign.
• IMPRODUCT — multiply by a conjugate.
• IMABS — compare magnitude.
• IMSUM — check distributivity over addition.

This is a Gnumeric tutorial, not a formula transplanted from another spreadsheet. The Gnumeric 1.12 function manual documents the signature, argument meanings and listed errors [1]; the current official function catalogue lists this function as Complete / Basic (upstream status, not a test run here) [2]. The upstream 1.12.62 announcement describes improvements to complex-function Excel compatibility [3], but does not establish which older releases exhibit every behavior. The preferred distributed desktop environment is Linux/BSD; the project does not currently distribute Windows binaries [4].

All displayed results below are expected mathematical results independently checked, or directly documented error expectations. They are not observations from executing Gnumeric. Native tests, import/export round-trips and locale variants remain pending. The examples use the manual’s English function names, decimal points and comma argument separators; installed application locale/settings can affect formula entry and number display. Confirm your actual separators and formula editor on the target system before pasting formulas.

Official sources, checked 2026-10-13

1. Gnumeric 1.12 Complex function reference — Gnumeric-specific syntax, descriptions, optional defaults and documented errors; function sections are identified inline.
2. Gnumeric official function catalogue — catalogue presence and implementation/upstream test classifications, not runtime evidence for these worksheets.
3. Gnumeric 1.12.62 upstream release announcement — release-level version and complex-compatibility context; no per-example validation claimed.
4. Official Gnumeric download/platform guidance — supported distribution pathways as stated by maintainers.

Evidence boundary: The examples were independently calculated and checked against official documentation and the Gnumeric 1.12.62 source. Native execution, locale checks and file round-trips were not performed.