IMSIN in Collabora Office: Audit Complex Sine with Numeric Component Checks

• 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.

=IMSIN(Complex_number)

The Collabora reference accepts a complex string in a+bi or a+bj form. When the imaginary part is zero, the input may also be a numeric value. It explicitly says the output is always a string representing a complex number, with a zero part omitted from display.

For example, the documented numeric-input control =IMSIN(2) returns approximately 0.909297426825682 as text. The absent imaginary term does not make that function result an ordinary numeric scalar. Use a numeric component extractor when a subsequent step needs one.

Format A2:A5 as Text and enter exactly 0.5+0.75j, 2+j, 0.5-0.75j and 2j. Put =IMSIN(A2) in B2, then extract with =IMREAL(B2) in C2 and =IMAGINARY(B2) in D2. Fill all three down.

The displayed coefficients are rounded to nine decimals. B retains the complete calculated complex string; C and D expose its numeric coordinates.

The second row has a real sine coefficient greater than one. The familiar bound between −1 and one applies to real arguments, not arbitrary complex inputs. Clipping this output would change a valid result.

Collabora’s equation image states that sine of a+bj has real coefficient sin(a)×cosh(b) and imaginary coefficient cos(a)×sinh(b).

For the first input, independently check:

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

The expected values are 0.620704231 and 0.721650824, rounded. For a cell-driven control, replace 0.5 and 0.75 with IMREAL(A2) and IMAGINARY(A2).

IMREAL and IMAGINARY supply numeric coordinates. Ordinary SINH and COSH are helper functions in this identity; applying ordinary SIN separately to both coordinates is a different operation.

For a real 60-degree angle, use =IMSIN(COMPLEX(RADIANS(60);0;"j")). The independent real coefficient is 0.866025404, and the imaginary coefficient is zero. COMPLEX receives a radian value after the explicit conversion.

For input 2j, the real coefficient is zero and the imaginary coefficient is sinh(2), approximately 3.626860408. By contrast, the documented numeric input two represents a real two-radian angle and gives the real sine near 0.909297427.

A degree symbol in cell formatting does not change the numeric input’s unit. Likewise, having the coefficient two somewhere in the input does not make the two axes interchangeable.

Conjugating the first input from 0.5+0.75j to 0.5−0.75j preserves the real output and reverses the imaginary output. That is the first-versus-third-row control.

Negating both input coordinates gives −0.5−0.75j. Its sine has independently expected coefficients −0.620704231 and −0.721650824, because complex sine is odd. Negation and conjugation are different transformations.

For the numeric-input control, =IMREAL(IMSIN(2)) exposes the real coefficient as a number while =IMAGINARY(IMSIN(2)) exposes zero. This follows the documented string output plus the component functions’ separate contracts; it is not an assumption about how every aggregation coerces text.

For the first input, compare:

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

The independent target has real coefficient one and imaginary coefficient zero. The identity uses complete complex multiplication, including cross terms.

The sum of the two squared magnitudes is different: it equals cosh(1.5), approximately 2.352409615, for this input. IMCOS and IMSIN satisfy a complex square identity, not a claim that their magnitude squares always sum to one.

The official 4−3i control has coefficients approximately −7.61923172032141 and 6.548120040911, consistent with the same equation. The dedicated page also identifies the function in OpenDocument 1.2; that standard version does not establish Collabora’s original introduction release.

No complete malformed-string, mixed-suffix, blank-coercion or native overflow table is given. For these moderate calculations, compare numeric components against a declared tolerance such as 1e-9. That is a fixture check, not a universal precision guarantee.

• Collabora Office 26.04: IMSIN.
• 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.