PlanMaker IMAGINARY: Extract the imaginary coefficient and preserve its sign

The 2026 function reference, 2024 reference and 2021 reference were retrieved and read on October 15, 2026. They establish documented support in those PlanMaker manual families. The original introduction and any last-working-version endpoint remain unverified; 2021 is the oldest reference checked here, not an introduction claim. Specific FreeOffice/mobile builds and every desktop platform were not tested.

The tables combine documented function rules with independent component arithmetic and high-precision mathematical calculations. No native PlanMaker execution, screenshot, export or import test was performed. Complex result components are used where native string formatting is not established. English examples use commas between arguments; adapt locale syntax only after checking the installed editor.

ComplexNumber is one required argument, documented in x+yi or x+yj form. The official example =IMAGINARY("2+4i") returns 4. Use a quoted supported literal or a reference to a cell constructed with COMPLEX. There is no documented optional argument or default.

Create ImaginaryComponents with Real_input, Imag_input, Complex_value and Imag_result in A1:D1. Enter the numeric A:B pairs and fill C2 =COMPLEX(A2,B2) and D2 =IMAGINARY(C2) through row 8.

The extraction in D follows B regardless of A’s sign. Zero in D7 means the value is purely real; zero in D8 describes the imaginary part of the entirely zero value. D alone cannot distinguish those cases.

In a copy, change A3 from 3 to 30. D3 stays 4. In a second original copy, change B3 from 4 to -4. D3 becomes -4. These controls isolate which coefficient the function reads.

A quarter-turn counterclockwise maps a Cartesian point (x,y) to (-y,x). This is a mathematical transformation, not a claim that every complex-valued engineering field represents a geometric point. On the original worksheet, put E3 below, then extract its coefficients in F3 and G3:

E3: =COMPLEX(-IMAGINARY(C3),IMREAL(C3))
F3: =IMREAL(E3)
G3: =IMAGINARY(E3)

The original row-3 value has coefficients (3,4), so the rotated coefficients are (-4,3). =IMABS(C3) and =IMABS(E3) are both mathematically 5. The real and imaginary coefficients change, but the Euclidean magnitude remains fixed.

Apply the same construction to E3 for a second quarter-turn: =COMPLEX(-IMAGINARY(E3),IMREAL(E3)). Its coefficients become (-3,-4). A third application gives (4,-3) and a fourth returns (3,4). Keep each intermediate result in a separate cell when testing the sequence.

On another sheet construct (3,4), (6,-2), (-1,-2) in C2:C4 using visible real/imaginary source columns. =IMSUM(C2,C3,C4) has coefficients (8,0). The separate coefficient sum =IMAGINARY(C2)+IMAGINARY(C3)+IMAGINARY(C4) is 0.

That cancellation does not mean all input imaginary coefficients were zero. If the middle imaginary coefficient changes from -2 to -1, the total becomes (8,1). Preserving the source components lets you identify the change instead of only seeing a different final representation.

Do not append i or j to the extracted numeric result before ordinary arithmetic unless you intend to reconstruct a complex representation. For reconstruction, COMPLEX keeps the intended coefficient positions explicit. Its optional suffix may be supplied if j notation must be retained.

The reference establishes the supported form, not every possible parser spelling, space, case or error token. Avoid assuming that formula text, plain numeric text and arbitrary imported strings are all accepted identically. IMREAL extracts the other coefficient; IMABS combines both into magnitude.

Record the exact product/build, edition, platform, locale and workbook format. Enter the full source table, inspect components and apply the changed-input controls on separate copies. Keep full precision for calculations and round only the display. Saved-file recalculation and destination compatibility require their own tests.