PlanMaker IMLN: Read complex log magnitude and phase separately

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.

=IMLN(ComplexNumber)

One complex argument is required. The logarithm base is e and is not an optional second argument. The short manual does not define a full principal-branch or negative-axis endpoint contract; this guide avoids those ambiguous native cases.

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 =IMLN(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 magnitude is √20 and its first-quadrant angle is arctan(2). Thus the logarithm has real coefficient ln(√20), approximately 1.497866137, and imaginary coefficient approximately 1.107148718. These agree with the vendor’s displayed 1.497866136777+1.10714871779409i within rounding.

For 3+4i, the magnitude is 5, so the real coefficient is ln(5), approximately 1.609437912. Taking ln(3) would ignore the imaginary input. In a copy replace A5:B5 with 6,8. The real coefficient becomes 2.302585093, while the imaginary coefficient remains approximately 0.927295218. Positive scaling changes magnitude but preserves direction.

Create LogRecovery. Put =COMPLEX(0.5,0.75) in A2 and =IMEXP(A2) in B2. The independent B2 coefficients are approximately 1.206351002 and 1.123832323. C2 =IMLN(B2) is expected to recover (0.5,0.75) on this selected first-quadrant case.

This restricted round trip must not be promoted to an identity for all imaginary inputs. Complex exponentials repeat when their imaginary arguments differ by a full turn, whereas a single-valued logarithm chooses one representative. The brief product reference does not settle every branch boundary or displayed endpoint.

Put =COMPLEX(3,4) in F2 and =COMPLEX(30,40) in G2. Subtract their logarithms with =IMSUB(IMLN(G2),IMLN(F2)). The expected coefficients are (ln(10),0), approximately (2.302585093,0). The scale factor ten is positive, so no phase change occurs in these inputs.

For a real magnitude reconstruction, =EXP(IMREAL(IMLN(F2))) is mathematically 5. It recovers magnitude, not the entire original complex number. Restoring the full value also needs the angle from the imaginary coefficient and the appropriate trigonometric reconstruction.

When reviewing a model, keep the original complex value, magnitude and chosen angular convention visible. A log magnitude alone cannot distinguish two inputs with the same modulus and different directions. Zero has no finite complex logarithm; the exact native error and negative-axis branch behavior remain unverified 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.