PlanMaker IMABS: Calculate complex magnitude and check cancellation
IMABS returns the modulus of a complex number. For coefficients x and y, its mathematical value is the nonnegative square root of x²+y². It combines both components; it is not the absolute value of only the real coefficient.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
IMABS returns the modulus of a complex number. For coefficients x and y, its mathematical value is the nonnegative square root of x²+y². It combines both components; it is not the absolute value of only the real coefficient.
Availability and evidence
The 2026 function reference, 2024 reference and 2021 reference were retrieved and read on October 15, 2026. They establish documented support in those PlanMaker manual families. The original introduction and any last-working-version endpoint remain unverified; 2021 is the oldest reference checked here, not an introduction claim. Specific FreeOffice/mobile builds and every desktop platform were not tested.
The tables combine documented function rules with independent component arithmetic and high-precision mathematical calculations. No native PlanMaker execution, screenshot, export or import test was performed. Complex result components are used where native string formatting is not established. English examples use commas between arguments; adapt locale syntax only after checking the installed editor.
Exact syntax
=IMABS(ComplexNumber)
Syntax and the vendor’s rounded example
ComplexNumber is required, with the documented x+yi or x+yj notation. No optional parameter is documented. SoftMaker shows =IMABS("2+4i") as 4.47214, a rounded presentation of √20. The independently computed value to nine decimals is 4.472135955; a different number of displayed decimals need not indicate a different underlying value.
Reproducible magnitudes from visible components
Create Magnitudes with Real, Imaginary, Complex_value, Modulus and Direct_check in A1:E1. Fill C2 =COMPLEX(A2,B2), D2 =IMABS(C2) and E2 =SQRT(A2^2+B2^2) through row 9.
| Row | A | B | Expected D/E |
|---|---|---|---|
| 2 | 2 | 4 | 4.472135955 |
| 3 | 3 | 4 | 5 |
| 4 | -3 | 4 | 5 |
| 5 | -3 | -4 | 5 |
| 6 | 5 | 12 | 13 |
| 7 | 0 | 5 | 5 |
| 8 | 5 | 0 | 5 |
| 9 | 0 | 0 | 0 |
The sign flips in rows 3:5 do not change magnitude. Row 9 is mathematically safe for IMABS: its modulus is zero. That does not establish the behavior of IMARGUMENT at zero, where a direction is not defined.
In a copy, change B3 from 4 to 12. D3/E3 become √153, approximately 12.369316877. In another original copy, multiply both A3 and B3 by 2. Its magnitude becomes 10, double the original 5.
Advanced: magnitude of a sum versus sum of magnitudes
Create two complex values in A2 and A3 using =COMPLEX(3,4) and =COMPLEX(-3,4). Put B2 =IMSUM(A2,A3), B3 =IMABS(B2) and B4 =IMABS(A2)+IMABS(A3). The sum has coefficients (0,8), B3 is 8, and B4 is 10.
Adding the individual magnitudes loses direction information. It is therefore not a substitute for adding complex values and then measuring the result. The mathematical triangle inequality gives magnitude(sum) no greater than sum(magnitudes), but equality does not generally hold.
On a copy, replace A3 with =COMPLEX(-3,-4). The two values cancel, so B2 has coefficients (0,0), B3 becomes 0, while B4 stays 10. In another original copy, use =COMPLEX(6,8) for A3: the aligned values sum to (9,12), giving B3=15 and B4=15. These three controls distinguish cancellation, differing direction and alignment.
Numerical and interpretation cautions
The direct SQRT(x²+y²) expression is a transparent audit on these small values. It is not a guaranteed numerically identical implementation for extreme coefficients: squaring can overflow even where a better-scaled magnitude algorithm could succeed. No internal algorithm or native overflow threshold is asserted here.
A modulus has the same unit as the represented components when both components use the same unit. Combining unrelated units in one complex number would not make their modulus meaningful. The examples are mathematical vectors, not measurements certified for an engineering application.
Malformed complex strings, mixed suffix conventions, numeric-text conversion and exact invalid-input errors are outside the checked cases. IMREAL and IMAGINARY expose the coefficients; IMARGUMENT describes direction. Neither coefficient alone supplies the modulus.
Verify in an installed version
Record the exact product/build, edition, platform, locale and workbook format. Enter the full source table, inspect components and apply the changed-input controls on separate copies. Keep full precision for calculations and round only the display. Saved-file recalculation and destination compatibility require their own tests.