IMCOS in WPS Spreadsheet: Calculate Cosine of a Complex Argument

=IMCOS(inumber)

The required input is complex text. The official formula image gives:

cos(x+yi) = cos(x) cosh(y) - i sin(x) sinh(y)

The real trigonometric argument x is in radians. Hyperbolic cosine and sine depend on the imaginary coefficient y. This function is not the cosine of the magnitude sqrt(x²+y²), and it does not separately take ordinary cosine of both coefficients.

Enter text 1+2i in A2 and use =IMCOS(A2) in B2. The independent calculation is:

• Real component: cos(1)×cosh(2) ≈ 2.032723007020.
• Imaginary coefficient: −sin(1)×sinh(2) ≈ −3.051897799152.

Thus the expected complex value is approximately 2.032723007020−3.051897799152i. This states the mathematical components; it does not promise the exact digits or string format produced by an untested WPS build.

Use =IMCOS("0+1i") as a simpler control. Since cos(0)=1 and sin(0)=0, the result is cosh(1) with zero imaginary coefficient. With =IMCOS("0+0i"), the mathematical result is 1.

The sign change between the first two rows follows from cosine being even and sine being odd in the real argument. These controls expose a sign mistake in the imaginary term without needing to assume any vendor-specific rounding rule.

A complex argument combines oscillation in x with hyperbolic growth in y. For x=0, increasing |y| increases cosh(y), explaining why a value above 1 is perfectly consistent with complex cosine. It is not evidence that the result should be clipped to the interval −1 to 1.

For an ordinary real angle measured in degrees, convert that angle to radians before constructing the real component. Do not automatically apply a degree conversion to an arbitrary imaginary coefficient: its meaning comes from the model that supplied the complex input.

The entire complex cosine has no logarithm-style branch cut. That mathematical fact does not remove parser limitations or numerical overflow risks. Hyperbolic terms can grow quickly for large |y|, so this guide uses small coefficients and does not establish the build’s extreme-input range or error behavior.

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 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 lesson explicitly states that a logical input gives #VALUE!. With Boolean TRUE stored in A2, =IMCOS(A2) therefore has that documentation-based error expectation; it has not been executed here.

The official WPS Academy IMCOS lesson, published 2019-06-19, explicitly applies to WPS Office for Windows Personal. It was reviewed on October 18, 2026. 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.

• COS: calculate cosine of a real radian argument.
• COSH: inspect the real hyperbolic factor.
• IMCONJUGATE: compare a conjugate transformation.