PlanMaker IMDIV: Divide complex values with a denominator check

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.

=IMDIV(ComplexNumber1, ComplexNumber2)

Both complex arguments are required. There is no optional default. ComplexNumber1 is the numerator and ComplexNumber2 the denominator; the worksheet deliberately keeps the denominator nonzero.

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 =IMDIV(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.

For (a+bi)/(c+di), the real coefficient is (ac+bd)/(c²+d²), and the imaginary coefficient is (bc−ad)/(c²+d²). The common denominator is a real squared magnitude, not c+d.

For the documented =IMDIV("4+12i","2+4i"), c²+d²=20. The real numerator is 4×2+12×4=56 and the imaginary numerator is 12×2−4×4=8. The quotient is therefore 2.8+0.4i. In a copy reverse those two operands: the quotient becomes 0.35−0.05i, rather than the original result.

Create GainRecovery. Put =COMPLEX(3,4) in A2 as a supplied input and =COMPLEX(6,8) in B2 as its output. C2 =IMDIV(B2,A2) has expected coefficients (2,0). D2 =IMPRODUCT(C2,A2) reconstructs B2’s (6,8).

In a copy replace B2 with =COMPLEX(-8,6). The quotient has coefficients (0,2), and reconstruction gives (−8,6). Both gains have magnitude 2, but their phases differ. A magnitude-only comparison would miss the quarter-turn in the second transformation.

This worksheet assumes the input/output pair and mathematical orientation have been specified. The function does not establish a physical transfer model, units, sign convention or the reliability of measured data.

Put =COMPLEX(1,0) in F2 and =COMPLEX(0.1,0) in G2. =IMDIV(F2,G2) is mathematically 10. Changing G2 to =COMPLEX(0.01,0) produces 100. A tenfold reduction in denominator magnitude multiplies the quotient by ten.

Keep denominator magnitude visible with =IMABS(G2) when interpreting a ratio. A nonzero denominator can still be too small for a stable practical calculation. The help does not give an application-specific minimum magnitude or an exact native error token for a zero complex denominator; neither is invented here.

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.