IMSUB Function (Gnumeric)

IMSUB(z1,z2) returns the difference z1 - z2, subtracting the real parts and imaginary parts separately. If z1 = a+bi and z2 = c+di, the difference is (a-c)+(b-d)i. Use it to compare complex measurements, calculate an error vector, or inspect changes in amplitude-and-phase representations without stripping away the imaginary component [1, IMSUB].

Version-specific error distinction: The online 1.12 manual describes malformed complex inputs as #VALUE!. The official 1.12.62 source instead returns #NUM! when parsing a malformed complex string; other unsupported value types can still return #VALUE!. Any #VALUE! expectations below are the manual’s older documented rule, not verified 1.12.62 output. No native error test was performed.

Exact Gnumeric syntax

=IMSUB(z1,z2)

The Gnumeric manual defines exactly two positional arguments, each a complex value. It documents #VALUE! if either is invalid [1, IMSUB]. Unlike Gnumeric’s IMSUM(z1,z2,...), IMSUB has no documented variadic argument form. Additional subtractions can be nested.

Independently expected G2: (3+4i)-(1-2i)=(3-1)+(4-(-2))i=2+6i. The sign of the second number’s imaginary component matters: subtracting -2i adds 2i. The formula, arguments and invalid-input error type are documented for Gnumeric [1, IMSUB]. Exact spaces or zero terms in the displayed complex result remain untested.

Additional formulas and mathematical expectations

As with any complex-number function, distinguish an algebraically expected value from the application’s exact printed representation. The text "2+6i" is a convenient notation, not an assertion about Gnumeric’s formatting of every sign and zero.

Suppose the measured response is 3+4i and the reference is 1-2i. Their complex deviation is 2+6i. Put the difference =IMSUB(E2,F2) in G2 and use =IMABS(G2) in H2. Independently, the magnitude of the error vector is sqrt(2²+6²)=sqrt(40)≈6.3245553203 [1, IMABS]. This gives an interpretable scalar error size without discarding the original complex direction. To preserve direction, add =IMARGUMENT(G2) in I2, producing an independently expected angle atan2(6,2)≈1.2490457724 radians [1, IMARGUMENT].

This is a mathematical worksheet illustration, not a validated instrument tolerance or acceptance criterion. Define an allowable magnitude using the real-world process, not an arbitrary threshold in the tutorial.

Gnumeric documents IMSUM for adding complex numbers [1, IMSUM]. Starting with an original value E2, subtract a baseline F2 into G2, then calculate =IMSUM(G2,F2) in H2. Algebraically H2 should return E2. Check the difference using =IMABS(IMSUB(H2,E2)), with a mathematical expectation of zero. Do not compare stringified complex-number outputs when floating-point rounding is possible.

To subtract a sequence of adjustments, use nesting: =IMSUB(IMSUB(E2,F2),F3) represents (E2-F2)-F3, not E2-(F2-F3). If the user instead wishes to subtract the sum of the baseline values, an equivalent algebraic form is =IMSUB(E2,IMSUM(F2,F3)). The latter references Gnumeric’s documented IMSUM variadic form [1, IMSUM] and is easier to audit when row counts vary.

This is a guide to Gnumeric, based on the Gnumeric 1.12 manual [1]. Gnumeric’s own function catalogue [2] lists IMSUB 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, IMSUB]. This means a function-level description rather than validation of cell-formatting or undocumented argument coercions; 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].

• IMSUM — sum complex values.
• COMPLEX — construct a complex number.
• IMABS — measure size of a complex difference.
• IMARGUMENT — measure direction of the difference.
• IMDIV — normalize by a reference.

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.