IMEXP in WPS Spreadsheet: Evaluate the Complex Exponential
Calculate e raised to complex text in WPS Spreadsheet using independent real and imaginary components, with magnitude and phase explanations.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =IMEXP("1+2i") has expected mathematical value approximately −1.131204383757+2.471726672005i. The real coefficient controls magnitude through e¹, while the imaginary coefficient supplies a radian angle of 2.
Syntax and identity
=IMEXP(inumber)
The one required input is complex text. The official identity is:
e^(x+yi) = e^x (cos(y) + i sin(y))
Here y is interpreted in radians. This is the exponential of the whole complex number, not e raised separately to each coefficient. The mathematical magnitude is e^x; cosine and sine distribute that magnitude across real and imaginary components.
Worked example: reproduce the two components
- Enter text 1+2i in A2 on a fresh worksheet.
- Enter
=IMEXP(A2)in B2. - Independently calculate e×cos(2) ≈ −1.131204383757.
- Independently calculate e×sin(2) ≈ 2.471726672005.
- Compare the resulting complex value with those components, allowing for display rounding.
The lesson’s WPS walkthrough includes this input. A separate illustration in the same article explicitly refers to an Excel worksheet; that illustration is not evidence of WPS runtime output. The original calculations here rely on the stated identity and are not an execution report.
Useful mathematical controls
| Formula | Expected real component | Expected imaginary coefficient |
|---|---|---|
=IMEXP("0+0i") |
1 | 0 |
=IMEXP("0+1i") |
0.540302305868 | 0.841470984808 |
=IMEXP("3+4i") |
−13.128783081462 | −15.200784463068 |
=IMEXP("-3+4i") |
−0.032542999640 | −0.037678977575 |
The zero case is the identity e⁰=1. The second row lies on the unit circle because its real coefficient x is zero. The last two rows share angle 4 but have magnitudes e³ and e⁻³, respectively. The table reports components rather than exact serialized complex strings.
Advanced use: magnitude and angle checks
For 1+2i, squaring the two output components and adding them gives e², apart from rounding in a decimal approximation. Taking the square root returns e, approximately 2.718281828459. This provides an independent magnitude check on a copied result.
Changing the imaginary coefficient by a full mathematical turn of 2π leaves the exact complex exponential unchanged. A finite decimal approximation to 2π will introduce numerical differences, so equality of displayed text is not an appropriate general test of that identity. Retain adequate intermediate precision.
The exponential itself is single-valued. Recovering an angle from its result is a different problem: angles that differ by full turns produce the same point, so the output does not uniquely preserve the original imaginary coefficient. This guide does not infer a complex-logarithm branch convention or promise an inverse round trip.
Large positive real coefficients can produce very large magnitudes, while large negative ones produce small magnitudes. The cited lesson does not establish numerical overflow, underflow or a fixed precision tolerance for WPS; use the small controls above before interpreting extreme results.
Input handling and output checks
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.
Evidence and version scope
The official WPS Academy IMEXP 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.