IMSQRT in Collabora Office: Find and Check Square Roots of Complex Values
Use Collabora IMSQRT with complex text, verify roots by squaring their components, and distinguish the returned root from the second mathematical solution.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =IMSQRT("3+4i") has documented result 2+1i. Squaring 2+i gives 3+4i, because (2+i)²=4+4i−1.
Syntax and input representation
=IMSQRT("ComplexNumber")
ComplexNumber is the required complex value, entered in x+yi or x+yj form. Quote a literal complex string, or refer to a cell containing the text. The function returns a complex square-root value, not the ordinary square root of the magnitude alone.
The dedicated section provides the 3+4i→2+1i control but does not fully specify branch-cut, zero, or formatting behavior. The examples here use first-quadrant inputs whose positive-real, positive-imaginary root agrees with that documented control.
Exact text spelling may vary, for example whether a coefficient one is shown explicitly. The table below gives mathematical values rather than asserting every native output-string character.
Example: build four independently verifiable roots
Enter these complex values as text in A2:A5. In B2 use =IMSQRT(A2) and fill down.
| A: input | B: independent root value |
|---|---|
| 3+4i | 2+i |
| 5+12j | 3+2j |
| 8+6i | 3+i |
| 7+24j | 4+3j |
The first row is the vendor’s documented control. The remaining values are independently checked complex roots under the same first-quadrant choice; no native Collabora execution is claimed.
For a root a+bi, its square has real component a²−b² and imaginary component 2ab. Thus 3+2j squares to 5+12j, and 4+3j squares to 7+24j.
Check with the spreadsheet’s complex multiplication
In C2 use =IMPRODUCT(B2;B2) and fill down. The independent expected mathematical values are the original inputs 3+4i, 5+12j, 8+6i, and 7+24j.
IMPRODUCT handles complex multiplication. A comparison based only on raw text can be misleading if mathematically equal values use different spellings, such as 2+i versus 2+1i. Inspect real and imaginary components for a numerical audit.
Use IMREAL and IMAGINARY to extract those components. Then compare the reconstructed square’s components with the original ones, allowing a justified floating-point tolerance rather than demanding every displayed character match.
Advanced example: distinguish square root from magnitude
The magnitude of 3+4i is 5. The magnitude of its root 2+i is √5, approximately 2.236067977. The root itself is still 2+i, not the real number √5.
A magnitude-only calculation discards direction. Replacing IMSQRT with =SQRT(IMABS(A2)) would return the root’s magnitude for this example, not the complex square-root value. IMABS is useful for checking lengths, while IMSQRT preserves a complex result.
Advanced mathematical limitation: there are two roots
If z=2+i satisfies z²=3+4i, then −z=−2−i also satisfies the same equation. The function returns one value, as illustrated by its documented positive-root control; it does not return a two-cell list containing both roots.
When solving a mathematical equation that needs both solutions, record both z and −z as solutions after verifying the first root. This does not establish the native function’s choice for every complex-plane boundary. In particular, branch behavior for negative-real-axis or signed-zero inputs is not documented by the short section reviewed here.
Errors and troubleshooting
Check that a literal complex value is quoted, that the text follows the documented i or j form, and that a cell reference is not accidentally quoted as the text “A2”. Keep units and suffix notation consistent when combining results with other complex functions.
The source does not enumerate a full native coercion/error matrix or extreme numerical limits. An invalid complex string is not an ordinary negative-number case for the real SQRT function. Validate the supplied first-quadrant controls before generalizing to a larger numerical model, and retain the original values for auditing.
Availability and verification
The exact function is documented in Collabora Office 26.04 desktop help, retrieved and reviewed on October 17, 2026. This establishes a documentation scope, not the first release that introduced the function or the last version in which it works; those versions and any retirement date remain unestablished. Collabora Online and mobile support are not inferred from desktop help, nor is behavior in another spreadsheet product.
The examples are documentation-based expectations with independent calculations. They have not been executed in Collabora Office. No application screenshot or native error/coercion certification is implied. Formulas use English function names and semicolon argument separators.
References
- Collabora Office 26.04: IMSQRT (checked October 17, 2026).
- Editorial testing standards.