IMCOS in Collabora Office: Keep the Imaginary Minus Sign in Complex Cosine

• Introduced: the original Collabora release and launch date are not established by the reviewed sources.
• Availability: documented in Collabora Office 26.04 desktop help.
• Platform scope: online and mobile deployment support is not inferred from the desktop documentation.
• Checked: October 14, 2026. Function-specific documentation and independent controls; no native Collabora execution.

=IMCOS(Complex_number)

Collabora accepts complex text in a+bi or a+bj form. A purely real input may be supplied as a numeric value as well. The dedicated reference explicitly states that the returned complex representation is a string, even when a zero component is omitted.

Its numeric control =IMCOS(2) returns approximately −0.416146836547142 as text. A result that looks like a decimal number therefore still needs an appropriate numeric component step when used as a numeric measurement.

Format A2:A5 as Text and enter 0.5+0.75j, 2+j, 0.5-0.75j and 2j. Calculate B2 with =IMCOS(A2), C2 with =IMREAL(B2) and D2 with =IMAGINARY(B2). Fill down.

These nine-decimal coefficients are independent expected displays. Retain B’s actual calculated value for later formulas rather than reconstructing from the printed rounded columns.

The last row is a complex argument on the imaginary axis, even though its cosine is purely real. Its real coefficient exceeds one; imposing the real-argument cosine bound would be incorrect.

Collabora’s equation gives cos(a)×cosh(b) as the real coefficient and negative sin(a)×sinh(b) as the imaginary coefficient.

For the first input, use:

=COS(0.5)*COSH(0.75)
=-SIN(0.5)*SINH(0.75)

Expected numbers are approximately 1.136191474 and −0.394239642. Leaving out the minus sign produces the conjugate of the intended answer for this fixture.

A cell-driven check uses IMREAL(A2) for a and IMAGINARY(A2) for b. Ordinary trigonometric helpers take radians; the hyperbolic helpers apply to the imaginary coefficient in this identity.

=IMCOS(COMPLEX(RADIANS(30);0;"j")) has independent real coefficient 0.866025404 and zero imaginary coefficient. It models a real thirty-degree angle after converting it to radians.

=IMCOS("2j") instead has real coefficient cosh(2), approximately 3.762195691. Its input is purely imaginary. The fact that both outputs have no imaginary component does not make the original inputs equivalent.

Use =IMREAL(IMCOS(2)) to expose the documented real numeric-input control as a number, and IMAGINARY to obtain its zero imaginary coefficient. This explicit extraction avoids relying on an unverified text-to-number rule elsewhere in a workbook.

Cosine is even in the independent complex model. Negating both coordinates of 0.5+0.75j gives −0.5−0.75j and leaves the cosine unchanged: 1.136191474−0.394239642j, shown approximately.

Conjugating only the imaginary coordinate gives 0.5−0.75j and reverses the output’s imaginary sign. The third row demonstrates that different operation.

This gives two useful audit controls: one for a complete input negation and one for conjugation. Neither should be replaced by blindly negating the output.

For A2, calculate:

=IMSUM(IMPRODUCT(IMCOS(A2);IMCOS(A2));IMPRODUCT(IMSIN(A2);IMSIN(A2)))

The independently expected quantity is one, with zero imaginary coefficient. IMPRODUCT retains the imaginary-square and cross terms needed for this identity.

If the checking procedure squares only the real coefficients, it misses the rest of the complex square. If it instead adds squared magnitudes, the result for this input is approximately 2.352409615, equal to cosh(1.5), rather than one.

IMSIN provides the other complex term. Keep the complete operations explicit so a correct magnitude calculation is not mistaken for a different identity.

The documented =IMCOS("4-3i") output has coefficients approximately −6.58066304055116 and −7.58155274274654. Both signs agree with the same equation for those coordinates.

The page identifies the function as part of OpenDocument 1.2, without establishing the original Collabora release. It does not provide a complete invalid-string, logical-value, mixed-suffix or error-precedence table. Those details are not imported from Excel.

Use explicit component tolerances for moderate examples. Extreme hyperbolic growth can cause numerical trouble, but no native threshold or exact overflow error is certified by these calculations.

• Collabora Office 26.04: IMCOS.
• Editorial testing standards.

Complete dedicated reference and its equation image reviewed. Examples are independently calculated controls or explicit documented statements, not native application captures. Formulas use English names and semicolon separators.