IMINV Function in Gnumeric: Complex Reciprocal
Find a complex reciprocal in Gnumeric, convert impedance to admittance, and check near-zero risks.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =IMINV("3+4i") calculates the reciprocal, with expected value 0.12-0.16i. The input must be nonzero.
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 IMINV does
For z=a+bi, the reciprocal is (a−bi)/(a²+b²). Its magnitude is 1/|z|, and its phase has the opposite sign modulo a full turn. A useful application is converting complex impedance Z into admittance Y=1/Z. The spreadsheet does not attach physical units to the result. Function reference.
Syntax and inputs
=IMINV(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:
=IMINV("1+2i")
=IMINV(COMPLEX(1,2))
=IMINV(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 =IMINV(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" |
=IMINV(A2) |
0.500000000 − 0.500000000i |
A3: "1-i" |
=IMINV(A3) |
0.500000000 + 0.500000000i |
A4: "3+4i" |
=IMINV(A4) |
0.120000000 − 0.160000000i |
A5: "-2-3i" |
=IMINV(A5) |
-0.153846154 + 0.230769231i |
A6: "1-2i" |
=IMINV(A6) |
0.200000000 + 0.400000000i |
A7: "2" |
=IMINV(A7) |
0.500000000 |
A8: "0.5" |
=IMINV(A8) |
2.000000000 |
A9: "1-j" |
=IMINV(A9) |
0.500000000 + 0.500000000i |
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: impedance to admittance
Put 3+4i in A2 as an impedance in ohms and enter =IMINV(A2) in B2. The expected admittance is 0.12-0.16i siemens. =IMREAL(B2) gives conductance 0.12; =IMAGINARY(B2) gives susceptance −0.16. Resistance/reactance and conductance/susceptance are different quantities.
Check the reciprocal with =IMPRODUCT(A2,B2), which should represent 1. The residual =IMABS(IMSUB(IMPRODUCT(A2,B2),"1")) should be near zero. Compare coefficients or residuals rather than text strings, and choose a tolerance appropriate to the input scale.
Zero has no reciprocal. Very small magnitudes produce very large reciprocals and can magnify input uncertainty or overflow. Do not confuse IMINV with IMNEG, IMDIV (a general complex quotient), or MINVERSE (a matrix inverse).
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.
Invalid numerical outputs are mapped to a numeric error by the release implementation. Avoid evaluating at the mathematical poles described above; an error token is not a substitute for checking the model’s domain.