PlanMaker IMPOWER: Raise complex values to explicit integer powers
IMPOWER raises a complex number to an exponent. This guide uses positive integer exponents, for which repeated complex multiplication gives an unambiguous independent reference. Fractional powers need a separately verified branch convention.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
IMPOWER raises a complex number to an exponent. This guide uses positive integer exponents, for which repeated complex multiplication gives an unambiguous independent reference. Fractional powers need a separately verified branch convention.
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
=IMPOWER(ComplexNumber, Exponent)
Both the complex base and Exponent are required. No optional exponent is documented. A one-argument IMPOWER call is therefore not a valid replacement for the two-argument syntax shown here.
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, imaginary coefficient in B and Exponent in C. Use D2 =COMPLEX(A2,B2) and E2 =IMPOWER(D2,C2). Inspect F2 =IMREAL(E2) and G2 =IMAGINARY(E2). Fill through row 7.
| Row | A | B | C | Expected F | Expected G |
|---|---|---|---|---|---|
| 2 | 2 | 4 | 2 | -12.000000000 | 16.000000000 |
| 3 | 3 | 4 | 2 | -7.000000000 | 24.000000000 |
| 4 | 1 | 1 | 3 | -2.000000000 | 2.000000000 |
| 5 | 0 | 1 | 4 | 1.000000000 | 0.000000000 |
| 6 | 2 | 0 | 3 | 8.000000000 | 0.000000000 |
| 7 | 1 | -1 | 2 | 0.000000000 | -2.000000000 |
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.
Square the vendor input without dropping cross terms
The documented =IMPOWER("2+4i",2) returns −12+16i. The real coefficient is 2²−4²=−12, and the imaginary coefficient is 2×2×4=16. Squaring the two coefficients independently would not compute the square of the complex number.
For row 3, (3+4i)²=−7+24i. Its magnitude is 25, the square of the original magnitude 5. In a copy change C3, the exponent, from 2 to 3. E3 becomes −117+44i, with magnitude 125. The imaginary coefficient 44 is not obtained by cubing 4 alone.
Advanced: separate repeated rotation from growth
On UnitPowers, use real coefficient 0.8 in A2 and imaginary coefficient 0.6 in B2. This base has magnitude 1 because 0.8²+0.6²=1. Put exponents 1,2,3 in D2:D4 and fill E2 =IMPOWER(COMPLEX($A$2,$B$2),D2) downward.
Expected coefficient pairs are (0.8,0.6), (0.28,0.96), (−0.352,0.936). Their squared magnitudes are all 1. Repeated powers change direction without changing magnitude for this chosen unit base. That conclusion follows from the base’s magnitude; it is not true for every complex input.
Compare with a base 3+4i: its powers 1,2,3 have magnitudes 5,25,125. Increasing an integer exponent changes scale as well as phase when the starting magnitude differs from one. This is useful when reviewing repeated mathematical transformations or a discretely compounded complex gain.
A four-step cycle as a separate control
For base COMPLEX(0,1), exponents 1,2,3,4 have coefficient pairs (0,1), (−1,0), (0,−1), (1,0). The fourth power returns real 1. A real result does not imply the function discarded the imaginary part incorrectly; it can be the correct result of the whole expression.
Do not extend these integer controls to a universal claim about fractional exponents, negative exponents, a zero base, or 0^0. The short reference does not settle those cases. Compare repeated multiplication only when the exponent and original inputs are actually the same.
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.