IMDIV Function (Gnumeric)

IMDIV divides the first complex-number input by the second: mathematically z1 / z2. It is useful for a ratio of complex measurements, normalization against a reference, impedance calculations, and checking relative amplitude and phase [1, IMDIV]. Its argument order is consequential: IMDIV(A2,B2) is generally not the same as IMDIV(B2,A2).

=IMDIV(z1,z2)

The official manual lists two arguments and documents #VALUE! if either is not a valid complex number [1, IMDIV]. The complex number may be produced by COMPLEX(x,y) or represented as notation such as "3+4i". There is no optional parameter, default denominator, or variable-length argument list in the documented signature.

Enter two complex measurements as explicit coefficients. This avoids assuming that ordinary numeric cell arithmetic directly handles complex text.

Independent arithmetic using a conjugate gives (3+4i)/(1-2i) = ((3+4i)(1+2i))/(1²+2²) = (-5+10i)/5 = -1+2i. Therefore G2 is expected to represent -1+2i, subject to Gnumeric’s display formatting. These are mathematical calculations; no Gnumeric execution is claimed. The specific quotient signature comes from the Gnumeric manual [1, IMDIV].

Smaller formula examples

The second row’s algebraic answer is unambiguous, but whether a bare numeric 2 is accepted as a complex argument for a particular build should be verified before calling it an observed application output. Use COMPLEX(2,0) to make this test independent of implicit conversion.

Suppose a reference sample is 3-4i and a new sample is 3+4i. Put =COMPLEX(3,4) in A2 and =COMPLEX(3,-4) in B2, then =IMDIV(A2,B2) in C2. The independently calculated ratio is -0.28+0.96i. Its magnitude is 1 because numerator and denominator both have magnitude 5; =IMABS(C2) can check this relationship [1, IMABS]. Its phase is approximately 1.854590436... radians by independent atan2(0.96,-0.28) arithmetic; =IMARGUMENT(C2) is documented to return such a phase in radians [1, IMARGUMENT].

This separates relative amplitude from relative phase, helping distinguish a sign or rotation change from a change in size. Do not use a fixed-size ratio as proof of physical calibration without a real measurement model.

After calculating G2 = IMDIV(E2,F2), put =IMPRODUCT(G2,F2) in H2. Algebraically this should recover 3+4i [1, IMPRODUCT]. Compare with E2 by applying IMSUB(H2,E2) and IMABS to the difference; the mathematical residual is 0, but real floating-point implementations can show small errors. A robust report would use a tolerance rather than demand identical strings.

For batches of observations, copy the paired numerator and denominator formula down the worksheet while maintaining the same row alignment. Check denominators before computing ratios; complex zero means both components are zero. IMABS(F2)=0 is a useful inspection formula, although precise error propagation for zero division has not been established by the cited IMDIV manual text.

This is a guide to Gnumeric, based on the Gnumeric 1.12 manual [1]. Gnumeric’s own function catalogue [2] lists IMDIV as Complete / Basic: the first term reports catalogue implementation classification; the second is the project’s test-suite category. Neither is a record of running the examples in this tutorial. The 1.12.62 release announcement [3] mentions improved compatibility for complex-number functions generally, but does not assert this tutorial’s examples were tested, nor identify every supported older release.

The official Gnumeric manual explicitly labels this function Microsoft Excel compatible [1, IMDIV]. This means only a declared function-level compatibility category; precise division-by-zero results, text coercion, i/j formatting and file interoperability remain unverified; it is not proof of byte-for-byte identical imports, worksheet display, coercion of blanks, text-number conversion, or localized formula entry in Microsoft Excel. Do not infer compatibility from another spreadsheet’s identically named function.

The formulas here use Gnumeric’s English-language function names, a period for the decimal separator, and commas between arguments. The Gnumeric 1.12 manual illustrates commas as function-argument separators [5]; its locale documentation explains that numeric conventions are influenced by system locale [6]. Confirm the actual installation’s formula editor and locale before pasting examples or changing separators. Gnumeric’s download guidance describes Linux/BSD distributor packages as the usual installation route and says the project does not currently distribute Windows binaries [4]. This does not prove a function works on every platform or build.

A complex number such as "3+4i" is passed as text notation to the complex-function family. A different unit suffix (i versus j), case, spaces, Unicode minus signs, explicit empty strings, missing cells, and errors are possible parsing or coercion edge cases; the official function reference is not a complete acceptance matrix. This page does not claim those cases were executed. Use COMPLEX(real,imaginary) to construct consistently formed values when possible [1, COMPLEX].

• IMPRODUCT — multiply complex numbers.
• IMABS — measure magnitude.
• IMARGUMENT — calculate phase angle.
• IMSUB — calculate complex residual.
• COMPLEX — build well-formed inputs.

1. Gnumeric 1.12: Complex-function reference — canonical signature, specific argument meanings and documented errors; function sections noted inline above.
2. Gnumeric function catalogue — presence, implementation label and upstream test-suite classification; not independent execution of this guide.
3. Gnumeric 1.12.62 release announcement — announced release context and general complex-number compatibility improvements.
4. Gnumeric official download and platform guidance — distribution routes and lack of currently distributed Windows binaries.
5. Gnumeric 1.12: types of cell elements / using functions — documented function-form and comma argument separator for the English examples.
6. Gnumeric 1.12: languages and locales — locale behaviour and numeric formatting context.

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.