IMNEG Function in Gnumeric: Complex Negation
Negate both parts of a complex number in Gnumeric, with cancellation checks and sign examples.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =IMNEG("2-3i") returns the additive inverse, -2+3i. Both coefficients change sign.
Availability and version history
- Introduced: 1.1.6, according to the official release history. This was a development-series release.
- 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. Source and independently calculated examples checked; Gnumeric 1.12.62 was not run.
What IMNEG does
For z=a+bi, IMNEG returns −a−bi. Use it to cancel an offset, subtract a complex contribution, or reverse a signal. It preserves magnitude; for a nonzero value its phase changes by π radians modulo 2π. Negation is different from conjugation: the conjugate changes only the imaginary coefficient. Function reference.
Syntax and inputs
=IMNEG(z)
z is one required complex number: a quoted complex string, a cell holding one, or the result of COMPLEX(real,imaginary). There is no second argument or default value. For example:
=IMNEG("1+2i")
=IMNEG(COMPLEX(1,2))
=IMNEG(A2)
Quote a literal such as "1+2i"; do not enter a bare 1+2i expression. COMPLEX accepts an optional i/j suffix. The examples use comma separators inside multi-argument functions; local formula conventions can differ.
Worked examples
Put the indicated complex text in A2:A9, without the outer quotation marks; prefix an apostrophe if needed to preserve text. Enter =IMNEG(A2) in B2 and fill down. The table gives mathematical reference values rounded to nine decimal places.
| Complex input (as formula literal) | Corresponding Gnumeric formula | Expected mathematical result (approximately) |
|---|---|---|
A2: "1+i" |
=IMNEG(A2) |
-1.000000000 − 1.000000000i |
A3: "1-i" |
=IMNEG(A3) |
-1.000000000 + 1.000000000i |
A4: "3+4i" |
=IMNEG(A4) |
-3.000000000 − 4.000000000i |
A5: "-2-3i" |
=IMNEG(A5) |
2.000000000 + 3.000000000i |
A6: "1-2i" |
=IMNEG(A6) |
-1.000000000 + 2.000000000i |
A7: "2" |
=IMNEG(A7) |
-2.000000000 |
A8: "0" |
=IMNEG(A8) |
0.000000000 |
A9: "1-j" |
=IMNEG(A9) |
-1.000000000 + 1.000000000i |
Use =IMREAL(B2) and =IMAGINARY(B2) to compare coefficients. A different i/j suffix or display precision does not by itself change the complex value.
Example: cancel a complex offset
Put the offset 2-3i in A2 and =IMNEG(A2) in B2. The correction is -2+3i. Enter =IMSUM(A2,B2) in C2: the mathematical sum is zero. Use =IMREAL(B2) and =IMAGINARY(B2) to inspect the correction’s coefficients, −2 and 3.
The same pattern works for a complex sensor bias or a balancing contribution, provided the quantities use matching units and sign conventions. Keep the measured value in A2 rather than overwriting it.
Check the operation you intended
With 1+2i in A2, =IMNEG(A2) should represent -1-2i. =IMABS(IMSUM(A2,IMNEG(A2))) is a cancellation check with expected value zero. Applying IMNEG twice recovers the original complex value. IMINV instead calculates 1/z; it is not a substitute for negation.
Input errors and practical checks
The 1.12.62 complex parser maps malformed complex text to #NUM!, whereas the web manual’s generic invalid-input note says #VALUE!. The pinned parser rejects other unsupported types with #VALUE!; coercion before that helper can affect blanks or Booleans. Use an explicit complex string or COMPLEX result when diagnosing an input problem.
Negation itself has no pole or branch cut. The common mistakes are negating only one coefficient, confusing negation with conjugation, or asking ordinary text arithmetic to interpret the complex value.