PlanMaker IMPRODUCT: Multiply complex values and inspect both coefficients

The PlanMaker 2026 reference, 2024 reference and 2021 reference were retrieved and read on October 15, 2026. They establish documented support in those manual families, not the original introduction or a last-working-version endpoint. Both historical endpoints remain unverified; specific FreeOffice/mobile editions and every desktop build are outside the checked scope.

No native PlanMaker execution, screenshot or workbook export was performed. Numerical expectations are independent mathematical calculations. English formulas use commas between arguments; check localized names and separators in the installed build.

=IMPRODUCT(ComplexNum1 [, ComplexNum2, ComplexNum3 ...])

The first complex argument is required and further arguments are optional. The reference does not state a maximum argument count or a complete cell-range flattening contract. The guide uses two explicitly supplied operands, with a separate three-operand control.

The documented inputs are complex numbers written in x+yi or x+yj form. A literal such as "2+4i" needs quotation marks in a formula. The COMPLEX reference supplies a safer construction method when real and imaginary coefficients occupy separate numeric cells. Its default suffix is lowercase i; lowercase j is an alternative.

The worksheets use COMPLEX with its default i suffix. They compare the returned value through IMREAL and IMAGINARY, rather than requiring an exact text spelling, spacing or number of trailing zeroes. A zero imaginary coefficient might be displayed more simply by the application; a mathematically real result is still a valid outcome of a complex calculation. Mixed i/j inputs and parser variants are outside the verified scope.

Create ComplexValues with real/imaginary coefficients for the first operand in A:B and for the second in C:D. Use E2 =COMPLEX(A2,B2), F2 =COMPLEX(C2,D2) and G2 =IMPRODUCT(E2,F2). Inspect H2 =IMREAL(G2) and I2 =IMAGINARY(G2). Fill all formulas through row 7.

Enter the numeric coefficient columns exactly as shown. Expected components are rounded to nine decimal places for comparison; they are not observed native strings or a promised implementation precision.

The documented =IMPRODUCT("2+4i","1+2i") returns −6+8i. The real part is 2×1−4×2=−6; the imaginary part is 2×2+4×1=8. Multiplying just the real coefficients and just the imaginary coefficients would incorrectly produce 2+8i.

For row 3, the operands 3+4i and 3−4i are conjugates. Their product is real 25, since 3²+4²=25. That is not the magnitude 5; it is the squared magnitude. In a copy change D3 from −4 to 4. G3 becomes −7+24i instead of 25. The sign of the imaginary coefficient changes the operation materially.

On Rotations, enter =COMPLEX(3,4) in A2 and =COMPLEX(0,1) in B2. Enter C2 =IMPRODUCT(A2,B2), D2 =IMPRODUCT(C2,B2), E2 =IMPRODUCT(D2,B2) and F2 =IMPRODUCT(E2,B2).

The coefficient pairs are (−4,3), (−3,−4), (4,−3), (3,4). Each step preserves magnitude 5 and rotates the represented vector by a quarter-turn. Inspect coefficients using IMREAL/IMAGINARY in spare cells; do not add or multiply the displayed strings as ordinary text.

This is a chosen mathematical transformation, not evidence about a device’s phase convention. If a receiving system defines clockwise rotation as positive, the appropriate multiplier may differ. Repeating the calculation four times gives a useful round-trip control for the supplied mathematical convention.

Use =IMPRODUCT(COMPLEX(3,4),COMPLEX(1,1),COMPLEX(2,0)). The independently expected coefficients are −2 and 14. The first product is −1+7i, then multiplication by 2 scales both coefficients. Grouping those same operands as nested two-argument calls gives the same mathematical result.

Finite-precision implementations need not produce byte-identical formatted strings for every regrouping. Compare coefficients with a tolerance chosen for the input scale. A matching small example does not prove a universal argument limit or exact associativity of floating-point arithmetic.

Check the input coefficients, argument order and actual formulas before changing display precision. A quoted cell address is text, not the referenced cell. Keep complex construction and coefficient inspection separate from ordinary text concatenation.

The short reference does not specify every coercion, mixed-suffix, blank, array, extreme-value or malformed-input error case. Do not import an error token or parser behavior from another spreadsheet. Record the exact PlanMaker build, edition, platform, language and file format before native testing. Recreate the original fixture, apply each changed-input control to a copy, then verify save/reopen and any destination format separately.