IMABS Function (Gnumeric)

IMABS gives the modulus (distance from the origin) of a complex number. For z = a+bi, |z| = √(a²+b²), a nonnegative real-valued magnitude. It is useful for phasor magnitudes, signal gain, AC impedance magnitude and geometric distance in the complex plane. It is not the absolute value of each coefficient separately.

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.

Official syntax and argument

=IMABS(z)

z is the complex number to measure. It is a single required argument; no default or optional mode is documented. The Gnumeric 1.12 manual documents #VALUE! for invalid complex arguments. There is no unit conversion: if the input represents ohms, the magnitude represents ohms.

Reproducible worksheet

Independent arithmetic: |2+3i|=√(2²+3²)=√13≈3.6055512755; |1−2i|=√5≈2.2360679775; |3+4i|=√(9+16)=5. Values shown are expected numerical values, not Gnumeric screenshots or runtime tests.

Additional examples and geometry

• =IMABS("0+0i") → 0 (origin).
• =IMABS("-3+4i") → 5 (signs of individual coefficients do not make magnitude negative).
• If C2=COMPLEX(2,3), compare =IMABS(C2)^2 to =IMREAL(C2)^2+IMAGINARY(C2)^2 → 13 mathematically; floating point may yield a nearby value instead of exactly 13.

Advanced application: gain or impedance magnitude

For impedance Z=R+iX in ohms, put resistance in A2, reactance in B2, and =COMPLEX(A2,B2) in C2. =IMABS(C2) gives |Z|. With R=2 and X=3, the expected magnitude is √13 ohms. The separate phase angle is not the modulus; use a phase/argument analysis when direction is required.

For complex transfer factors C2 and C3, verify the multiplicative identity |C2*C3|=|C2||C3| using IMPRODUCT and two IMABS calls, recognizing normal floating-point tolerance.

Troubleshooting and limits

Compatibility

The official manual labels IMABS Excel-compatible. The public catalogue lists an upstream Complete/Exhaustive test classification, which is stronger metadata than several related functions but does not mean these worksheets were executed here, nor does it guarantee the same results on all platforms and locales.

These examples are independently calculated expectations, not observed output from a running Gnumeric installation. The published Gnumeric 1.12 manual documents the function’s signature and relevant error behavior, and the Gnumeric project’s function catalogue records upstream implementation and test classifications. The official 1.12.62 release announcement confirms that release exists (September 2026). The live manual/catalogue are not immutable 1.12.62 source-code snapshots, so document coverage must not be confused with runtime verification of every locale, platform, or build.

The examples use the English function names and the comma separators shown in the official manual. Your localized Gnumeric configuration might use another argument separator or decimal notation; use its Function Browser to confirm the accepted local entry format. Complex-number strings in the examples use the i suffix consistently. The Gnumeric manual also documents COMPLEX’s j suffix option, but do not mix conventions in one calculation without validating that workflow in your installation. Gnumeric is generally distributed through Linux/Unix-like systems and source packages; the project does not provide current official Windows binaries.

• COMPLEX — construct consistent a+bi input strings from coefficients.

• IMREAL — extract the real coefficient.

• IMAGINARY — extract the imaginary coefficient.

• IMSUM — add complex values.

• IMPRODUCT — multiply complex values.

• IMPOWER — raise a complex value to a power.

1. Gnumeric Manual 1.12 — Complex functions: documented purpose, signature, argument meanings, #VALUE! notes, Excel-compatibility label and cross-references for IMABS. Dynamic 1.12-series documentation, not a pinned release source tree.
2. Official Gnumeric function catalogue: imabs listed as Complete implementation with Exhaustive upstream test classification; that describes upstream project metadata, not execution of this worksheet. The live catalogue currently presents an aggregate count that differs from the 1.12.62 release registry, so it is not used to assert catalogue completeness.
3. Gnumeric 1.12.62 official release announcement: release existence and Excel/complex-function compatibility work (the release announcement does not guarantee each example or Excel round-trip).
4. GNOME official 1.12 source-release directory: official versioned source distribution; the official 1.12.62 source was inspected for this review.

Evidence categories: official-manual documentation checks; official-catalogue metadata checks; independent arithmetic checks. Not performed: native function execution, locale-specific execution, Excel comparisons, GUI screenshots, or application screenshots.