IMREAL Function (Gnumeric)
Learn the IMREAL function in Gnumeric: Returns the real coefficient of a complex number.
Verification status: Official documentation referenced; example outcomes independently reasoned or arithmetically checked where stated. Not executed in Gnumeric. How formula examples are checked
IMREAL returns the real part of a complex value. For the complex number 3+4i, the real coefficient is 3, regardless of the size of the imaginary coefficient. This is different from the magnitude: IMABS("3+4i") has the independently calculated result 5. Gnumeric documents both in its own Complex manual [1, IMREAL / IMABS].
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
=IMREAL(z)
| Argument | Required? | Meaning | Default |
|---|---|---|---|
z |
Yes | A valid complex number, such as a recognized complex-number string, a reference to a complex result, or the output from COMPLEX. |
None |
Gnumeric documents one argument only. The return value is a real numeric coefficient; the function does not return the complex number unchanged and does not calculate its absolute value. The official manual specifies #VALUE! when z is not a valid complex number [1, IMREAL]. Do not add optional arguments because another spreadsheet has them.
Reproduce a worksheet step by step
Enter this worksheet data:
| Cell | Input | Explanation |
|---|---|---|
| A1 | Complex input |
Header |
| B1 | Real coefficient |
Header |
| A2 | 3+4i |
Complex-number text; if Gnumeric interprets direct typing differently, enter it as "3+4i" in a formula or build with COMPLEX. |
| B2 | =IMREAL(A2) |
Extract the real coefficient. |
| A3 | =COMPLEX(-2,5) |
Generated complex value. |
| B3 | =IMREAL(A3) |
Extract a negative real coefficient. |
Expected: B2 = 3; B3 = -2. For a reproducible formula not dependent on a cell’s text-entry interpretation, replace A2 with =COMPLEX(3,4) or use =IMREAL("3+4i") directly. The expected numbers follow the complex-number definition, and the function signature comes from Gnumeric’s official manual [1]. No Gnumeric worksheet was run during this review.
Formula-focused examples
| Formula | Independently expected result | Interpretation |
|---|---|---|
=IMREAL("3+4i") |
3 | Discards the imaginary part as a coefficient extraction. |
=IMREAL("3-4j") |
3 | j is the supported alternative imaginary unit in the complex family. |
=IMREAL(COMPLEX(-2,5)) |
-2 | Works with a generated complex value. |
=IMREAL(IMCONJUGATE("3+4i")) |
3 | Complex conjugation preserves the real coefficient. |
=IMREAL(IMPRODUCT("3+4i","1-2i")) |
11 | Multiplication produces 11-2i. |
=IMREAL("not-a-complex-number") |
#VALUE! expected by documented invalid-complex rule |
Do not assume arbitrary text is convertible. |
When testing literal strings, type the double quotation marks in the formula, e.g. =IMREAL("3+4i"); do not put " characters into A2 as literal cell content. Gnumeric’s local string or numeric input conventions need actual application validation.
Real-world scenario: separate in-phase signal readings
Complex quantities are useful in signal-processing worksheets. Suppose A2=6 is the in-phase component and B2=-8 is the quadrature component. Put =COMPLEX(A2,B2) in C2. In D2 put =IMREAL(C2): the independently expected result is 6. In E2 put =IMAGINARY(C2): expected -8. In F2 put =IMABS(C2): expected SQRT(6^2+(-8)^2)=10.
Keeping those three quantities separate avoids a common reporting error: calling the real component the whole signal magnitude. The computations are a simple illustrative data model, not a calibrated measurement procedure. Copy the formulas down for additional rows, and compare extracted coefficients with the original input columns to audit data entry.
Advanced: independently audit a complex calculation
Let z1=3+4i and z2=1-2i. Complex multiplication distributes as
z1 × z2 = (3×1 - 4×(-2)) + (3×(-2)+4×1)i = 11 - 2i.
Use =IMREAL(IMPRODUCT(COMPLEX(3,4),COMPLEX(1,-2))). The real result should be 11. You can cross-check it from source coefficients with a plain numeric expression =3*1-4*(-2) (also 11). In an audit workbook, this gives a numeric independent check without depending on text formatting of the product.
To confirm conjugate symmetry, compare =IMREAL(COMPLEX(3,4)) and =IMREAL(IMCONJUGATE(COMPLEX(3,4))); both should be 3. That is a mathematical identity, not an observed Gnumeric unit test.
Errors, limits and troubleshooting
| Problem | Reason / investigation |
|---|---|
#VALUE! for malformed z |
Gnumeric explicitly documents this error when z is not a valid complex number [1]. Use a documented format or COMPLEX. |
| A positive result where a negative one was expected | Check the real input and signs in any preceding IMPRODUCT/IMSUM, not the imaginary coefficient. |
| IMREAL gives 3, IMABS gives 5 | Correct distinction for 3+4i: real coefficient versus modulus. |
Ordinary cell A2 seems to be parsed as something else |
Prefer =COMPLEX(3,4) in A2 or supply the quoted complex literal inside the formula. Direct cell-entry parser behavior is untested here. |
| Blank, boolean, locale-formatted, or unusual numeric input | The manual’s one-argument description does not establish the exact coercion for every cell type. Do not invent those results; normalize/validate before extraction. |
| Imaginary unit letter and separator issues | Gnumeric’s complex manual supports i/j through COMPLEX, but spacing, alternate glyphs and regional punctuation need a native local test. |
| A referenced formula itself contains an error | Trace the upstream cell first. This review does not claim a particular propagated error type beyond the manual’s documented invalid complex input case. |
Compatibility, edition and test boundary
The Gnumeric 1.12 manual labels IMREAL Excel compatible [1, IMREAL], and the official catalogue currently lists implementation Complete, upstream testing Basic [2]. Those statements do not prove import/export fidelity, every prior version, or native execution of these examples. The 1.12.62 announcement reports an improvement to Excel compatibility for complex functions without giving IMREAL-specific edge-case test outputs [3]. For an application-level check, include both imaginary-unit suffixes, COMPLEX-produced inputs, Unicode variants, purely real and imaginary inputs, malformed text, blanks, and an XLSX round trip.
Related Gnumeric guides
Software, version and evidence boundaries
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
- Gnumeric 1.12 Complex function reference — Gnumeric-specific syntax, descriptions, optional defaults and documented errors; function sections are identified inline.
- Gnumeric official function catalogue — catalogue presence and implementation/upstream test classifications, not runtime evidence for these worksheets.
- Gnumeric 1.12.62 upstream release announcement — release-level version and complex-compatibility context; no per-example validation claimed.
- 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.