PlanMaker IMSQRT: Check a complex square root by squaring it
IMSQRT returns a square root of a complex number. A nonzero complex value has two mathematical square roots. The examples here use positive real and positive imaginary input coefficients and the corresponding positive-coefficient root, consistent with the vendor example.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
IMSQRT returns a square root of a complex number. A nonzero complex value has two mathematical square roots. The examples here use positive real and positive imaginary input coefficients and the corresponding positive-coefficient root, consistent with the vendor example.
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
=IMSQRT(ComplexNumber)
One complex argument is required; there are no optional arguments. The short reference does not state a complete branch-cut or endpoint convention. Negative-axis and other branch-sensitive native cases remain unverified.
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 =IMSQRT(C2). Inspect E2 =IMREAL(D2) and F2 =IMAGINARY(D2). Fill through row 7.
| Row | A | B | Expected E | Expected F |
|---|---|---|---|---|
| 2 | 3 | 4 | 2.000000000 | 1.000000000 |
| 3 | 5 | 12 | 3.000000000 | 2.000000000 |
| 4 | 8 | 6 | 3.000000000 | 1.000000000 |
| 5 | 7 | 24 | 4.000000000 | 3.000000000 |
| 6 | 15 | 8 | 4.000000000 | 1.000000000 |
| 7 | 2 | 4 | 1.798907440 | 1.111785941 |
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.
Verify the documented result by reconstruction
SoftMaker gives the root of 2+4i as approximately 1.79890743994787+1.11178594050284i. Squaring those coefficients recovers the original value within rounding. A square-root check needs complex squaring, not squaring the coefficients separately and placing them back together.
For 3+4i, the expected root is 2+i because (2+i)²=(4−1)+4i. The other mathematical root is −2−i, which also squares to 3+4i. This observation does not claim that PlanMaker returns that second root or provides a selectable branch argument.
In a copy replace A2:B2 with 5,12. The expected root becomes 3+2i. Its square is 9−4+12i=5+12i. The same result already appears in row 3, providing a controlled repeat with identical inputs.
Advanced: reconstruct a supplied squared quantity
On RootResidual, put =COMPLEX(3,4) in A2, =IMSQRT(A2) in B2 and =IMPOWER(B2,2) in C2. Put =IMSUB(C2,A2) in D2 and inspect D2 with IMREAL and IMAGINARY. The independently expected residual coefficients are (0,0).
A small floating-point residual is more realistic than requiring an exact output string. Choose a tolerance suitable for the original scale and recorded implementation. A small reconstruction residual alone does not establish that the returned sign or branch matches a particular physical model: both square roots pass that same reconstruction test.
Independent coefficient construction on this domain
For x>0 and y>0, let r=√(x²+y²). The positive-coefficient mathematical root has real coefficient √((r+x)/2) and imaginary coefficient √((r−x)/2). For x=3,y=4, r=5, so the coefficients are √4=2 and √1=1.
For x=5,y=12, r=13 and the coefficients are √9=3 and √4=2. This derivation explains the two worksheet controls without importing an unverified negative-axis rule. It is a mathematical reference, not an alternate implementation certified over all floating-point inputs.
Keep the original quantity and any model-specific sign condition alongside the computed root. If the application needs a different mathematical branch, document and verify that requirement rather than assuming every square root is interchangeable.
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.