COMPLEX: Build Complex Numbers from Coefficients in WPS Spreadsheet
Construct complex text from real and imaginary coefficients with COMPLEX. Learn lowercase i and j suffixes, the default suffix and the lesson’s unresolved error-token conflict.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
COMPLEX constructs a complex-number text representation from two numeric coefficients. For a real coefficient of 5 and an imaginary coefficient of 2, the mathematical number is 5 + 2i. The second input is the coefficient 2, not the text "2i". Choosing "j" changes the notation to 5 + 2j without changing those coefficients.
This is useful when a table stores real and imaginary measurements in separate columns and you want a consistent representation for complex-number calculations. Keep the numeric source columns: they remain convenient for checking coefficients and applying ordinary arithmetic.
Syntax and a documentation warning
=COMPLEX(real_num, i_num, [suffix])
| Argument | Meaning |
|---|---|
real_num |
Required numeric real coefficient. |
i_num |
Required numeric imaginary coefficient. |
suffix |
Optional text suffix: lowercase "i" or "j". Omission means "i". |
The official lesson’s invalid-input guidance is internally inconsistent: its statements for nonnumeric coefficients and invalid suffixes concatenate #VALUE! and #REF!. It establishes which inputs to avoid, but does not establish one reliable error token for those cases. Neither token is presented here as a verified application result. Use numeric coefficients and the documented lowercase suffixes; uppercase "I" and "J" are not supported by the lesson’s contract. Official WPS lesson
The examples below use small positive integer coefficients. They do not establish serialization precision for arbitrary decimals, formatting of zero components, or coercion of numeric-looking text.
Build a column of complex text
Enter this original dataset as numbers:
| Cell | Value | Cell | Value |
|---|---|---|---|
| A2 | 5 | B2 | 2 |
| A3 | 7 | B3 | 3 |
| A4 | 6 | B4 | 4 |
- Put
=COMPLEX(A2,B2,"i")in C2. The documented construction gives5+2i. - Fill the formula down to C3 and C4, preserving the relative references. The corresponding text expectations are
7+3iand6+4i. - For j notation, use
=COMPLEX(A2,B2,"j"); the expectation is5+2j. - To use the documented default, enter
=COMPLEX(A2,B2); the expectation is5+2i.
These are documentation-derived expectations, not results from executing this workbook. The vendor walkthrough independently illustrates the default: its selected COMPLEX(A8,B8) uses coefficients 4 and 2 and displays 4+2i. That published example supports the construction rule; it is not a screenshot of the dataset above.
Small controls for coefficients and suffixes
| Formula | Expected text under the documented construction |
|---|---|
=COMPLEX(5,2,"i") |
5+2i |
=COMPLEX(7,3,"i") |
7+3i |
=COMPLEX(6,4,"i") |
6+4i |
=COMPLEX(5,2,"j") |
5+2j |
=COMPLEX(5,2) |
5+2i |
The same coefficient pair can therefore have two supported notations. This does not mean suffixes can be mixed freely in later calculations: the lesson says complex functions that accept multiple complex inputs require matching suffixes. Choose one convention for a complete dataset.
Practical case: combine components before construction
Suppose two fictional components have coefficients (5, 2) and (7, 3), stored in A2:B3 above. Their mathematical sum has real coefficient 5 + 7 = 12 and imaginary coefficient 2 + 3 = 5.
=COMPLEX(A2+A3,B2+B3,"i")
The resulting construction is 12+5i. This example uses ordinary numeric addition before COMPLEX; it does not concatenate the two strings or multiply their coefficients. For j notation, keep the same numeric calculation and replace the final suffix with "j", giving 12+5j.
As an independent mathematical check, the squared magnitude of 12 + 5i is 12² + 5² = 169, so its magnitude is 13. That check concerns the represented number; it is not an additional WPS execution claim. For calculations starting from complex text, see IMSUM and IMABS, whose own argument limits and input rules still apply.
Troubleshooting and boundaries
- Supply two numeric coefficients. An imaginary coefficient is a number such as 2; the suffix is supplied separately.
- Quote a literal suffix and keep it lowercase. The default is documented only for omission; an explicitly empty suffix is not treated here as equivalent.
- Keep suffixes consistent when passing multiple constructed values to complex functions.
- Do not diagnose an invalid input solely by expecting
#VALUE!or#REF!: the source mixes those tokens. The exact runtime error remains unresolved. - Very large values, decimal serialization, omitted required arguments and zero-component simplifications are outside the established examples. A displayed string should not be assumed to preserve unlimited numeric precision.
Availability and evidence scope
The official lesson is dated June 10, 2019 and explicitly identifies WPS Office for Windows Personal. It does not identify a numeric build. That date documents the lesson’s existence, not the function’s introduction; the first supported version and last working version remain unknown. The source does not establish Linux, other editions or current cross-platform parity, nor does it identify the function as retired or deprecated.
The lesson text and vendor walkthrough were inspected on October 18, 2026. Examples in this guide use independent coefficient arithmetic and the documented construction rule. They have not been executed in WPS or another calculation engine; no native screenshots or parser tests are claimed. Official syntax and walkthrough
Related: IMCONJUGATE changes the imaginary sign; IMPRODUCT multiplies complex inputs.