IMABS in WPS Spreadsheet: Measure the Magnitude of a Complex Number

=IMABS(inumber)

The one required argument is a complex number represented as text. The official formula image defines the modulus of x+yi as sqrt(x²+y²). Squaring the components removes their signs before the square root is taken. The result is a nonnegative real magnitude.

For 3+4i, the independent calculation is sqrt(9+16)=5. For −3+4i, it is still sqrt(9+16)=5. Equal magnitudes therefore do not establish that two complex numbers are equal or have the same direction.

Enter these text values in A2:A5 on a fresh worksheet. Put =IMABS(A2) in B2 and copy it down.

A literal control for A4 is =IMABS("1+2i"). Its noninteger result should be compared numerically with the mathematical value, not with an assumed number of displayed decimal places. Preserve enough digits for subsequent calculations and round only the presentation when appropriate.

The official lesson’s own walkthrough uses 13+4i; its displayed magnitude is consistent with sqrt(185). That historical illustration supports the meaning of the operation, while the table above is a separate, independently calculated example.

Suppose a two-component quantity has components 3 and 4 in the same unit. Its magnitude is 5 in that unit. Its squared magnitude is 25 in squared units. These are different summaries: use the first for a length-like result and the second only when the downstream model calls for a sum of squares.

For the opposite-sign point −3+4i, the magnitude remains 5. Thus a magnitude-only report loses directional information. Retain the original complex text or its real and imaginary components when signs or phase matter.

A useful independent consistency check is the conjugate identity: (3+4i)(3−4i)=25, which is the square of the magnitude. That is an algebraic cross-check, not a claim that a particular nested WPS expression was run. More generally, modulus combines orthogonal components; it is not the sum of their absolute values, which would be 7 in this example.

The zero input has mathematical magnitude zero and no directional information. No angle is needed to compute modulus, so these examples do not introduce a complex-logarithm or inverse-tangent branch convention. IMABS also does not decide whether the component units or measurement model are appropriate; those must already be consistent.

Pass a well-formed complex text value, such as "3+4i", or a cell containing that text. The WPS lesson describes x+yi and x+yj notation. These examples consistently use i; the imaginary unit is not a cell name or an unquoted variable. A cell reference supplies the stored complex text, whereas a quoted literal supplies the text directly.

The cited lesson does not provide a complete error or parsing table. Whitespace, uppercase suffixes, malformed expressions, locale-specific decimal punctuation, blank cells, logical values and array arguments are therefore outside the asserted examples. No Excel-derived error code or coercion rule is substituted for those gaps. Keep coefficients small when checking the examples; overflow and underflow behavior for extreme values is not established.

The official WPS Academy IMABS lesson, published 2019-05-06, explicitly applies to WPS Office for Windows Personal. It was reviewed on October 18, 2026. The narrative also names WPS 2019, which identifies the historical lesson context rather than a first release or exact build. The numeric build, introduction release and last supported version remain unknown. The source does not identify this function as deprecated or retired. Support in Linux, other editions and other platforms is not established by this lesson.

The worked examples are original mathematical expectations based on the official contract and formula illustration. They were not executed in WPS. Historical vendor demonstrations are documentation, not our application tests; no screenshot or runtime precision guarantee is supplied. English names and comma separators follow the lesson. Localized entry, workbook interchange and exact output formatting require verification in the intended client.

• IMCONJUGATE: reflect the imaginary component.
• ABS: take the absolute value of a real number.
• SQRT: compute a real square root.