IMSQRT in ONLYOFFICE: Complex Square Roots with Reproducible Examples

Real-only SQRT is documented as returning #NUM! for a negative real input; IMSQRT is for the complex-number representation and can produce an imaginary component. A complex number has the form a+bi or a+bj. For electrical engineering, signal processing and mathematical transformations, you often need a consistent branch for a square root of an impedance-like complex quantity. Do not discard the imaginary coefficient or silently replace a complex calculation with a real-only function. The official references define these functions separately: SQRT and IMSQRT.

Mathematically, the usual principal square root chooses a result with nonnegative real component, and a sign of the imaginary component determined by the original argument away from branch-cut ambiguities. This is a mathematical convention used to calculate the examples; the vendor’s brief function page does not explicitly specify branch-cut rules or signed-zero handling. Those runtime details still require testing.

=IMSQRT(inumber)

The function does not accept separate real and imaginary coefficients as two arguments. Build the single complex input with =COMPLEX(B2,C2) (vendor syntax: COMPLEX(real_num, i_num, [suffix]); suffix defaults to lowercase i and can be lowercase j). Quoted string literals such as "3+4i" are structurally different from unquoted spreadsheet expressions. The vendor function page does not enumerate every accepted text-conversion edge case. COMPLEX documentation.

1. Create a blank spreadsheet in an ONLYOFFICE Spreadsheet Editor edition you can identify. Use English formula language for the formulas below. Record your Desktop version or the actual Docs/server version and your region if you later report test results.
2. Enter the specified headers, then enter the table’s input values in the exact cells shown. Numeric inputs must be numeric cells (without quote marks). For complex inputs, use the documented COMPLEX constructor as directed.
3. Enter the formulas into the output cells exactly as shown, beginning with =. Use Formula → Function to find IMSQRT or type the function directly. Fill down only through the named last row; do not accidentally include table headers.
4. Compare your displayed values against the independently computed expected column. For decimals, change display format or use numeric tolerance rather than expecting identical trailing digits. For complex outputs, extract real and imaginary coefficients separately.
5. If your result differs, record the formula, underlying cell type, software platform/version, displayed result, separator/locale settings and any error without overwriting the expected-value reference. ONLYOFFICE’s formula-entry and recalculation guide describes recalculating via the Formula tab, or F9 for the workbook.

Set A1:I1 to Case, Real, Imaginary, Constructed complex, IMSQRT result, Expected real, Expected imaginary, Extracted real, Extracted imaginary. Put the B/C numeric coefficients shown below in rows 2–14, then enter =COMPLEX(B2,C2) into D2 and fill through D14. Put =IMSQRT(D2) into E2, fill E14. Enter the listed expected coefficients numerically in F/G. Use the vendor-documented =IMREAL(E2) in H2 and =IMAGINARY(E2) in I2 and fill to row 14. In J2, =AND(ABS(H2-F2)<0.00001,ABS(I2-G2)<0.00001) is a proposed numeric tolerance check, not a verified native result.

The complex output in column E might be displayed using i or j, with variable decimal formatting; no actual display strings were observed. The F/G columns contain mathematical expected coefficients, cross-checked with two independent complex arithmetic implementations. The last row is 14: do not accidentally compare against a header.

Two quick direct formulas

=IMSQRT(COMPLEX(3,4))
=IMSQRT(COMPLEX(-3,-4))

The first mathematically equals 2+i, and the second 1−2i. Check the coefficients rather than relying on text formatting. For a j-suffix construction, use =COMPLEX(3,4,"j") before passing that one argument to IMSQRT; j is vendor-documented for the constructor, but native propagation/display has not been tested here.

Square it back: =IMPRODUCT(E2,E2) is a documented way to multiply complex values. Mathematically, the result equals the original D2, up to numeric error. To compare precisely, extract IMREAL and IMAGINARY from both values. For the 3+4i row, multiplying 2+i by itself yields 3+4i. IMPRODUCT; IMREAL; IMAGINARY.

Magnitude identity: the magnitude of a square root satisfies |sqrt(z)|²=|z|. If your sample is in D8 and its expected square root in E8, compare the two numeric expressions =IMABS(E8)^2 and =IMABS(D8); each is expected to equal 5 for 3+4i. IMABS returns complex magnitude, not the same as taking the absolute value of just the real coefficient. IMABS.

Principal-branch derivation: Let z=a+bi, r=sqrt(a²+b²). For nonzero b, u=sqrt((r+a)/2) and v=sign(b) sqrt((r-a)/2). Then sqrt(z)=u+vi. At a negative real with imaginary coefficient zero, the principal result is positive imaginary, for example sqrt(-4)=2i. This formula is a mathematical derivation and is not a claim of observed ONLYOFFICE internal implementation. It also explains why merely applying SQRT(a) to the real part is wrong.

Create two input columns representing the real and imaginary components of your dimensionless normalized model. Compute COMPLEX, then IMSQRT, and extract the result’s two components. For a sequence from 3+4i to 3−4i, the expected results are conjugates. Comparing both component columns exposes sign mistakes that a formatted complex output might hide. Do not attach units to input strings such as "3 V+4i"; keep units in a separate header. Flag values near negative real branch boundaries for further native verification, where argument representation and finite precision may matter.

Do not invent an error value. Where a case is mathematically defined but the editor’s coercion/overflow handling is undocumented, record it as native behaviour unverified, not a guaranteed #VALUE!, #NUM! or other message.

Use COMPLEX to construct complex inputs, IMREAL and IMAGINARY to extract components, IMABS to inspect magnitude, IMPRODUCT for a round-trip, and SQRT for nonnegative ordinary numeric inputs.

Officially documented: The current, unversioned English ONLYOFFICE Docs Spreadsheet Editor function page for IMSQRT and Insert Function catalogue list IMSQRT as an Engineering function. Checked 2026-10-13 (UTC). This supports the existence, purpose and signature of the function in the documented editor; it is not proof of identical behaviour in all past web integrations, all Desktop Editors builds, or mobile versions.

First-supported version: Not established by this research. The vendor maintains distinct Docs release history and Desktop Editors release history. Their availability does not, by itself, identify the first supported release of IMSQRT. Desktop version compatibility: NOT NATIVELY TESTED; browser/web version compatibility: NOT NATIVELY TESTED; historical versions: UNKNOWN; imported workbook round-trip and specific file-format compatibility: NOT TESTED.

English formulas: Examples use an initial = and commas between arguments where necessary, following the official Insert Function instructions. Under File → Advanced Settings, the editor offers Formula Language, Region, and decimal/thousands separators (official Advanced Settings guide). Translated formula names, regional separators and localized decimal entry are not verified here. Do not blindly swap commas for semicolons or translate a function name unless checked in the actual target installation.

Evidence classification: Every result labelled expected is derived from independent mathematical or logical computation, never copied from an ONLYOFFICE screenshot or claimed to have been observed in a running editor. Native Desktop executions: 0. Native web executions: 0. Any error strings described as possible diagnostic are not observed output.