PlanMaker IMSIN: Evaluate complex sine and test its odd symmetry

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.

=IMSIN(ComplexNumber)

One complex argument is required. No optional argument or default is documented. The real coefficient in the independent sine/cosine identities is measured in radians, not degrees.

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 =IMSIN(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, SoftMaker gives approximately 24.8313058489464−11.3566127112182i. The output is not expected to be bounded by ±1 because the argument is not real. Dropping the imaginary coefficient before evaluation would compute a different function value.

For pure imaginary input i, sine is approximately 0+1.175201194i. A real-only sine at zero would give zero and miss that imaginary component. For real input 1, the sine is approximately 0.841470985 with zero imaginary coefficient.

In a copy change B5 from 1 to −1, keeping A5=1. The sine becomes approximately 1.298457581−0.634963915i. The real coefficient stays unchanged and the imaginary coefficient reverses, as expected from conjugation for these inputs.

Create SineSymmetry. Put =COMPLEX(1,1) in A2 and =COMPLEX(-1,-1) in B2. C2 =IMSIN(A2) has expected coefficients approximately (1.298457581,0.634963915). D2 =IMSIN(B2) has their negatives.

E2 =IMSUM(C2,D2) should have mathematical coefficients (0,0). Changing only one input coefficient is a different operation from negating the whole argument. Keep both input coefficients visible so a successful symmetry check cannot hide a wrong test setup.

This is a mathematical identity check, not evidence of exact floating-point cancellation in every application build. Inspect coefficient residuals at the original scale and choose an appropriate numeric tolerance.

On another sheet put =COMPLEX(1,1) in A2. Evaluate B2 =IMSIN(A2) and C2 =IMCOS(A2). D2 =IMSUM(IMPOWER(B2,2),IMPOWER(C2,2)) is mathematically 1+0i. Do not replace those complex powers with |sin(z)|² and |cos(z)|²; their sum for this input is approximately 3.762195691.

A second construction uses Euler’s identity. Multiplying z by i gives −1+i, so =IMEXP(COMPLEX(-1,1)) has expected coefficients approximately 0.198766110 and 0.309559876. The expression =IMSUM(IMCOS(A2),IMPRODUCT(COMPLEX(0,1),IMSIN(A2))) represents the same mathematical value.

That comparison checks several independently specified operations without claiming a physical wave model. Keep the angle units and sign convention explicit, and investigate large or tiny outputs before assuming a display format caused the difference. No native overflow boundary or arbitrary complex-text coercion rule was established.

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.