IMPRODUCT in Zoho Sheet: Multiply Complex Numbers and Ranges

=IMPRODUCT(complex_num; [complex_num1]; ...)

The vendor states that the first parameter can be a text or range. It does not document a maximum number of operands, edge-case coercion rules or the exact returned spelling for values with zero/one coefficients. If only one complex number is supplied, ordinary multiplication theory would leave it unchanged; test the actual Zoho display before relying on that edge case.

For two complex numbers (a+bj) and (c+dj), their product is (ac−bd) + (ad+bc)j. The negative sign comes from j² = −1. For the official example (2+3j)(1+2j), the real part is (2×1−3×2)=−4; the imaginary coefficient is (2×2+3×1)=7. Result: -4+7j. Multiplying the coefficients independently, or just adding them, would be wrong.

Use C2:C6 from the shared practice table and put the following formulas into D1:D7:

For D5, multiply the first two values to obtain −4+7j; then multiply by 3−2j: real part −12+14=2, imaginary coefficient 8+21=29. This provides a calculable check that does not rely on Zoho’s formatting conventions. For D6, (2+3j)(5j)=10j+15j²=−15+10j.

The vendor separately documents =IMPRODUCT("1-4i";"5+1i") → 9-19i. Keep both inputs in the same lowercase i notation if reproducing this example. Neither the vendor examples nor this guide establishes what happens if you mix i and j suffixes in a single multiplication.

1. Magnitude squared via conjugates. Multiplying z by conj(z) gives a real nonnegative result. With C2=2+3j, compute the mathematical expectation for:

=IMPRODUCT(C2;IMCONJUGATE(C2))

The real coefficient should be 13, and imaginary coefficient 0, because (2+3j)(2−3j)=4+9=13. The exact display may suppress the zero imaginary part. Verify the same value by =IMABS(C2)^2 as an independent check. The conflicting official IMCONJUGATE("1+4i") example makes native checking important for the i case; see the official IMCONJUGATE reference.

2. Complex gain applied in sequence. Suppose a signal is 2+3j, first-stage gain is 1+2j, and second-stage gain is 3−2j. The mathematical result is 2+29j. In a model use =IMPRODUCT(C2;C3;C4) instead of performing multiplication by hand. If stages may be missing, validate their source strings first; the vendor doesn’t describe how null or empty range cells are treated.

3. Range-based product auditing. For a contiguous list in C2:C4, the vendor’s text/range syntax supports entering =IMPRODUCT(C2:C4). This guide flags its expected mathematical result but does not claim that native range evaluation was tested. Compare it to the explicit three-operand formula to detect parsing, blank-cell, or hidden-text issues.

4. Numerical-component cross-check. Compute real and imaginary parts of the first product independently with =IMREAL(C2)*IMREAL(C3)-IMAGINARY(C2)*IMAGINARY(C3) and =IMREAL(C2)*IMAGINARY(C3)+IMAGINARY(C2)*IMREAL(C3). The expected numbers are −4 and 7. These are proposed Zoho worksheet formulas using separately documented functions, not recorded native executions.

Mistake: use IMSUM when the model calls for a product. Fix: identify whether you need addition of components or multiplication with cross terms. Mistake: assume j means a variable named J. Fix: keep complex arguments as strings generated by COMPLEX or entered literally. Mistake: forget the −bd real cross-term. Fix: work through the official 2+3j example before extending formulas. Mistake: pass an entire data table with labels into a range. Fix: restrict a range argument to just verified complex-value cells. Mistake: compare 0+13j-style strings instead of components. Fix: check both parts separately; an output may normalize its notation.

• Introduced: The original introduction version and date are not established by the checked sources.
• Availability: Currently documented in Zoho Sheet’s rolling web-service help; no numbered release or retirement endpoint is established.
• Scope: English-language web-service documentation. Mobile and offline-client parity is outside the verified scope.
• Checked: October 14, 2026, against the official IMPRODUCT reference. Documentation check; not a new native test.

This guide was checked against Zoho Sheet’s official English-language cloud help on October 13, 2026. Formula separators here follow the vendor’s semicolon syntax (;); square brackets in syntax indicate optional arguments, not characters to type. The quoted i and j suffixes represent the mathematical imaginary unit and distinguish text-form complex numbers from ordinary spreadsheet numerics. For reproducibility, all exercises specify the cells and the input strings.

Zoho’s workbook locale settings let the author choose language, decimal separator, grouping, date and currency formats. The vendor’s English formulas are the directly checked source; changes in local decimal display or how formulas are entered under another locale have not been natively tested here. Zoho’s complex function catalogue includes this function, but the accessed reference does not establish a first-supported software version, a minimum subscription tier, or identical behaviour on iOS, Android, Windows and macOS clients. These particulars are unverified, not presumed universal.

Testing distinction: The vendor’s documentation supplies syntax and published examples. Expected outputs for additional examples were computed independently with standard complex arithmetic (Python complex values for QA), not by executing Zoho Sheet. Formatting of results, coercion of unusual inputs, mixed i/j suffixes, and edge-case error codes remain subject to an authenticated Zoho workbook test. No screenshot or account-level execution is claimed.

Reusable practice sheet

Create a blank Zoho Sheet and enter this input table into A1:C6 exactly. Alternatively import the complex-number practice CSV, starting at A1. Column C holds explicit text, not formulas. Do not paste formula results as replacements for the inputs.

Check that the imported C2:C6 values are literal strings. A formula such as =COMPLEX(2;3;"j") is an alternative documented way of generating the text 2+3j, but do not place it in C2 unless you intentionally want to test nested formulas. Other functions in the family include COMPLEX, IMREAL, IMAGINARY, and IMABS; those individual vendor pages were checked on October 13. A textual numeric value such as "2+3j" should not be treated as an ordinary numeric cell.

The official Zoho reference lists the following general spreadsheet error explanations; it does not promise that every error below occurs for every invalid argument to this specific function.

The function reference does not exhaustively document treatment of blanks, arrays beyond examples, text spacing, uppercase suffixes, combinations of i and j, overflow/underflow, or every malformed complex string. Do not advertise a specific result or error code for those cases without a native test. The display might simplify a coefficient of zero or one (for example 0+5j to 5j), so compare complex values—not merely strings—when validating a workbook. Zoho’s standard function-help error tables are not independent evidence that Excel and Zoho behave identically.

1. In a signed-in Zoho Sheet cloud workbook using the English help syntax, enter the listed official example and record displayed result, stored type, and application context.
2. Repeat with the supplied cell references; check that the content in C2:C6 is interpreted as text.
3. Compare independent mathematical expectations with the vendor example; preserve any disagreement, including separators, plus/minus signs and normalizing of a zero term.
4. Run separate edge-case probes for empty input, malformed string, alternative suffixes and invalid types. Record the actual returned error or value rather than guessing.
5. Optionally compare another locale or application platform, recording its locale, account tier and client version; do not backfill an invented first-release version.

Source descriptions below distinguish vendor statements from mathematical reasoning. The cited official documentation was reviewed on October 13, 2026; neither publication dates nor minimum versions were asserted by those pages.

• Definition, syntax, examples, general error list and related functions: Zoho Sheet IMPRODUCT — checked 2026-10-13.
• Reusable source-cell construction: COMPLEX — checked 2026-10-13; the optional suffix defaults to lowercase i in the vendor example.
• Independent part/magnitude cross-checks: IMREAL, IMAGINARY, IMABS — checked 2026-10-13.
• Workbook display/locale choices: Zoho Sheet Locale and calculation settings — checked 2026-10-13.
• Function-category membership: Official Zoho Complex function index — checked 2026-10-13; the index contains 18 function titles, not a platform/version guarantee.

Official claim boundaries: The function reference directly supports the syntax, parameter descriptions and its own explicitly quoted example results. The other numerical examples, conjugate identities, transfer calculations and audit checks are mathematical predictions. Ambiguous i-suffix cases, zero handling, client/version/tier behaviour and output text normalization are not passed off as native test results.

• Build complex text with COMPLEX
• Extract the real coefficient with IMREAL
• Extract the imaginary coefficient with IMAGINARY
• Calculate magnitude with IMABS