IMAGINARY in Collabora Office: Extract Signed Imaginary Coefficients and Check Rotations

• Introduced: the original Collabora release and launch date are not established by the reviewed sources.
• Availability: documented in Collabora Office 26.04 desktop help.
• Platform scope: online and mobile deployment support is not inferred from the desktop documentation.
• Checked: October 14, 2026. Function-specific documentation and independent controls; no native Collabora execution.

=IMAGINARY("ComplexNumber")

The official section accepts complex values described as x+yi or x+yj and demonstrates =IMAGINARY("4+3j") returning three.

The returned coefficient keeps its sign. In 2−5j, the coefficient is −5. The term −5j is that coefficient multiplied by the imaginary unit; the coefficient itself is an ordinary real number.

The short Collabora source does not explicitly document a numeric-only input rule, blank coercion or a complete error table. The worked calls use complex text rather than importing another application’s numeric-input example.

Enter only the first text column in A2:A5. In B2 use =IMAGINARY(A2) and fill down.

=SUM(B2:B5) has expected numeric result 0. This is cancellation among signed coefficients, not evidence that every original value had zero imaginary part.

Taking absolute values first would give 8+4+5+7=24, answering a different question. Keep the sign when the model requires a directional coordinate.

In C2 use =IMREAL(A2) and fill down. Expected real coefficients are 6, −3, 2 and 0. Then enter =COMPLEX(C2;B2;"j") in D2 and fill down.

The reconstructed quantities are 6+8j, −3+4j, 2−5j and −7j. A simplified representation may omit a redundant zero real term without changing the two coefficients.

IMREAL supplies the coordinate missing from an imaginary-only report. For example, 6+8j and −3+8j have the same imaginary coefficient but are different values.

For each original record, calculate:

=IMAGINARY(IMCONJUGATE(A2))

Fill down. Expected results are −8, −4, 5 and 7. Adding each to its original B value gives zero.

IMCONJUGATE reverses the imaginary sign while retaining the real coefficient. It does not merely make every imaginary coefficient positive: the originally positive values become negative.

For 6+8j, multiplication by j sends the components (6,8) to (−8,6). Use the explicit complex factor:

=IMPRODUCT("6+8j";"0+1j")

The expected quantity is −8+6j, whose imaginary coefficient is six. Repeating that quarter-turn gives −6−8j, then 8−6j, then the original 6+8j.

This transformation shows why multiplying only the imaginary coefficient by one does not implement multiplication by the imaginary unit. Both coordinates participate and one changes sign.

For (6+8j)(2−j), the imaginary coefficient is 6×(−1)+8×2=10. The real coefficient is twenty, so the complete product is 20+10j.

=IMAGINARY(IMPRODUCT("6+8j";"2-j")) therefore has expected result ten. Multiplying only the imaginary coefficients would give −8, which is a different number.

IMPRODUCT applies the complete component identity. Numeric helper columns make the cross-terms and their signs easier to audit.

A legitimate zero imaginary coefficient can occur without a missing observation. For the explicit string “6+0j”, the independently expected coefficient is zero. This does not establish the same behavior for an empty cell or a noncomplex numeric input.

The examples keep lowercase j notation consistent. Mixed-suffix rules, malformed strings, native numeric precision and exact error precedence remain unverified. The outputs are independent component calculations under the documented complex-text contract.

• Collabora Office 26.04: IMAGINARY.
• Editorial testing standards.

Complete function-specific documentation reviewed. Outputs are independent complex-component models or explicit documented controls, not captured native application results. Formulas use English names and semicolon separators; optional-argument brackets describe syntax and are not typed into working formulas.