PlanMaker IMCOS: Evaluate complex cosine without real-only shortcuts

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.

=IMCOS(ComplexNumber)

One complex argument is required; no optional default is listed. The whole complex input is the argument. Do not discard its imaginary coefficient or apply an ordinary real COS call directly to a complex text string.

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 =IMCOS(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.

The documented input 2+4i gives approximately −11.3642347064011−24.8146514856342i. Its large coefficients do not violate the usual real-cosine range: that restriction applies to a real argument, whereas the imaginary component introduces hyperbolic factors.

For a purely imaginary input i, the cosine is real cosh(1), approximately 1.543080635. For real input 1, the result is approximately 0.540302306. A zero imaginary result can therefore arise from a genuinely complex input, not just from a missing argument.

In a copy change B5 from 1 to −1, keeping A5=1. The result is approximately 0.833730025+0.988897706i: the real coefficient stays the same and the imaginary coefficient changes sign. This follows from conjugation for the supplied arguments.

Create TrigCheck. A2 is =COMPLEX(1,1), B2 is =IMCOS(A2) and C2 is =IMSIN(A2). D2 is =IMSUM(IMPOWER(B2,2),IMPOWER(C2,2)). The expected coefficients of D2 are (1,0).

The squares in this identity are complex squares, not squared magnitudes. For this input, |cos(z)|²+|sin(z)|² is approximately 3.762195691, not 1. Replacing IMPOWER with separate magnitude-squaring changes the mathematical expression.

Inspect the real and imaginary residual of IMSUB(D2,COMPLEX(1,0)); mathematically both are zero. A native floating-point implementation may leave a small numerical residual. This consistency check is not a universal accuracy certificate or a tolerance recommendation for extreme inputs.

For z=1+i, cosine is approximately 0.833730025−0.988897706i. Negating the entire argument to −1−i leaves the cosine unchanged. Negating only the imaginary coefficient to 1−i instead conjugates the result.

These are different changed-input tests. Use COMPLEX to make each coefficient explicit rather than editing a display string by hand. In a mathematical model, changing the full argument and reversing only a growth or attenuation coefficient can have different meanings even though both edits introduce a minus sign.

No application-specific physical interpretation is inferred from this function. Verify angular units, the complex sign convention and input scaling before using its output in a larger model.

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.