PlanMaker IMEXP: Separate complex exponential growth and rotation
IMEXP evaluates the complex exponential. For z=x+yi, the independent identity exp(z)=exp(x)(cos(y)+i sin(y)) separates magnitude from direction. The imaginary coefficient y is interpreted in radians in that mathematical identity.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
IMEXP evaluates the complex exponential. For z=x+yi, the independent identity exp(z)=exp(x)(cos(y)+i sin(y)) separates magnitude from direction. The imaginary coefficient y is interpreted in radians in that mathematical identity.
Availability and evidence
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.
Exact syntax and arguments
=IMEXP(ComplexNumber)
One complex argument is required; no optional default is documented. The function returns the exponential of that whole value, not separate exponentials of its two coefficients.
Represent and inspect the result
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.
Complete coefficient worksheet
Create ComplexValues with real coefficient in A and imaginary coefficient in B. Use C2 =COMPLEX(A2,B2) and D2 =IMEXP(C2). Inspect E2 =IMREAL(D2) and F2 =IMAGINARY(D2). Fill through row 7.
| Row | A | B | Expected E | Expected F |
|---|---|---|---|---|
| 2 | 0 | 0 | 1.000000000 | 0.000000000 |
| 3 | 1 | 0 | 2.718281828 | 0.000000000 |
| 4 | 0 | 1 | 0.540302306 | 0.841470985 |
| 5 | 1 | 1 | 1.468693940 | 2.287355287 |
| 6 | -1 | 0.5 | 0.322844582 | 0.176370799 |
| 7 | 2 | 4 | -4.829809383 | -5.592056094 |
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.
Compare the vendor example with the identity
The reference gives =IMEXP("2+4i") as approximately −4.82980938326939−5.59205609364098i. Its magnitude is exp(2), approximately 7.389056099, even though both displayed coefficients are negative. The phase factor contains cos(4) and sin(4), not angles of 4 degrees.
In a copy change A5 from 1 to 2, leaving B5 equal to 1. The expected coefficients become 3.992324048 and 6.217676312. Both original coefficients are multiplied by e, while the mathematical direction remains the same. Changing the real and imaginary coefficients has different effects.
Advanced: build a specified decaying oscillation
Create DecayModel with t values 0,0.5,1,2 in F2:F5. Fill G2 =IMEXP(COMPLEX(-0.5*F2,2*F2)) downward. This is the explicitly supplied mathematical model exp((−0.5+2i)t), not a model inferred from the data.
| t | Expected real coefficient | Expected imaginary coefficient | Expected magnitude |
|---|---|---|---|
| 0 | 1.000000000 | 0.000000000 | 1.000000000 |
| 0.5 | 0.420787859 | 0.655338262 | 0.778800783 |
| 1 | -0.252405815 | 0.551516768 | 0.606530660 |
| 2 | -0.240462050 | -0.278412079 | 0.367879441 |
The magnitude decays as exp(−0.5t); the mathematical phase advances by 2t radians. At t=0 the result is real 1. The table does not promise that a phase-inspection function will display an unwrapped angle beyond its own principal interval.
Keep units and the sign convention explicit. If t is measured in seconds, the supplied scale coefficients must be compatible with that choice. IMEXP cannot decide whether a damped-oscillation model is appropriate for a physical signal.
Advanced: check multiplication against addition in the exponent
Let z=0.25+0.5i and w=−0.5+0.25i. The independent identity exp(z+w)=exp(z)exp(w) compares =IMEXP(COMPLEX(-0.25,0.75)) with =IMPRODUCT(IMEXP(COMPLEX(0.25,0.5)),IMEXP(COMPLEX(-0.5,0.25))).
Both have expected coefficients approximately 0.569839864 and 0.530860800. Inspect component differences rather than exact string equality. This consistency check does not establish overflow thresholds or accuracy for extreme real or imaginary inputs.
Troubleshooting and verification limits
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.