PlanMaker IMLOG2: Track complex doublings with the correct phase scale

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.

=IMLOG2(ComplexNumber)

One complex argument is required. The base is fixed at 2, with no optional base parameter. The short help page does not specify a full logarithm branch-cut convention or a native error token for every invalid input.

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 coefficient in A and imaginary coefficient in B. Use C2 =COMPLEX(A2,B2) and D2 =IMLOG2(C2). Inspect E2 =IMREAL(D2) and F2 =IMAGINARY(D2). Fill 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 2+4i, the reference gives approximately 2.16096404744368+1.59727796468811i. Its magnitude is √20. The real coefficient is log2(√20), and the imaginary coefficient is arctan(2)/ln(2). Both are dimensionless mathematical coefficients; the second is not directly a radian angle.

For 3+4i, the magnitude is 5 and the real coefficient is log2(5), approximately 2.321928095. In a copy change A5:B5 to 6,8. The real coefficient becomes 3.321928095, while the imaginary coefficient remains approximately 1.337804212. Scaling by two adds one to the real logarithm coefficient.

Create DoublingAudit with scale values 1,2,4,8 in F2:F5. Fill G2 =IMLOG2(COMPLEX(3*F2,4*F2)) downward. Inspect real and imaginary components in H and I with IMREAL and IMAGINARY.

The expected real coefficients are 2.321928095, 3.321928095, 4.321928095, 5.321928095. Every imaginary coefficient is approximately 1.337804212. The underlying magnitudes are 5,10,20,40, respectively. The additive log steps correspond to multiplicative scaling; they are not differences in the original physical units.

This is a representation audit for a specified positive scale sequence. It does not imply that a device uses binary gain steps or that rounded coefficients meet a measurement tolerance. Keep the original values and the scale factors when those facts matter.

For the original 3+4i value, =POWER(2,IMREAL(IMLOG2(COMPLEX(3,4)))) mathematically recovers magnitude 5. Multiplying its log imaginary coefficient by LN(2) gives approximately 0.927295218 radians, the same first-quadrant direction as the original input.

Subtracting the log of 3+4i from the log of 6+8i with IMSUB gives coefficients (1,0). No angle is added by a positive real scale factor. This does not justify arbitrary log identities across a branch cut, and it does not verify behavior at zero, on the negative real axis or for text that only resembles a complex number.

A log coefficient of zero is not necessarily a zero input: real input 1 has magnitude log2(1)=0. Keep the original input separate from its transformed display to avoid that confusion.

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.