IMCOT in Collabora Office: Check Complex Cotangent without Dividing Coordinates Separately

• 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.

=IMCOT(Complex_number)

Collabora accepts complex text in a+bi or a+bj form. A purely real input may also be a number. The reference describes the result as a complex string, including cases where a zero component is omitted.

Its numeric-input example =IMCOT(2) returns approximately −0.457657554360286 as text. Use IMREAL to obtain its numeric real coefficient; the scalar-looking display does not change the documented return representation.

Cotangent is the ratio of cosine to sine where sine is nonzero. It is not an inverse function that recovers an angle from a tangent value.

Format A2:A5 as Text and enter 0.5+0.75j, 2+j, 0.5-0.75j and 2j. Fill down =IMCOT(A2) in B, =IMREAL(B2) in C and =IMAGINARY(B2) in D.

The coefficients are independently calculated and rounded to nine decimals. Keep the complete calculated B values for subsequent formulas.

The first and third rows are conjugates. The negative imaginary sign for a positive imaginary-axis input is meaningful; cotangent on that axis is not simply ordinary COT applied to its imaginary coefficient.

For the same inputs, calculate:

=IMDIV(IMCOS(A2);IMSIN(A2))

The expected coefficients match the primary table. IMDIV uses the complete numerator and denominator, including cross terms and the denominator’s squared magnitude.

Dividing the real cosine coefficient by the real sine coefficient alone does not produce the complete cotangent. IMCOS and IMSIN provide inspectable intermediate quantities.

The reference’s equation has denominator cosh(2b)−cos(2a), real numerator sin(2a), and imaginary numerator negative sinh(2b).

For a=0.5 and b=0.75, check:

=SIN(1)/(COSH(1.5)-COS(1))
=-SINH(1.5)/(COSH(1.5)-COS(1))

Expected numbers are approximately 0.464360461 and −1.175029450. The imaginary minus sign distinguishes this equation from a superficially similar tangent formula.

This is a separate component calculation from the complete cosine-over-sine ratio. Agreement between the two provides a useful control on coefficient signs and argument placement.

For A2, multiply IMCOT(A2) by IMTAN(A2) with IMPRODUCT. The independently expected quantity is one, with zero imaginary coefficient. This reciprocal check is valid here because both relevant denominators are nonzero.

A second identity compares the complete square of cotangent plus one with the complete square of cosecant:

=IMSUM(IMPRODUCT(IMCOT(A2);IMCOT(A2));COMPLEX(1;0;"j"))
=IMPRODUCT(IMCSC(A2);IMCSC(A2))

Both independently expected results have coefficients approximately −0.165063571 and −1.091274433. The cotangent square itself is approximately −1.165063571−1.091274433j; adding one changes only its real coefficient.

These are complex squares, not squares of magnitudes. Retain both coordinates when checking the identity.

For inputs j and 2j, the cotangent model gives approximately −1.313035285j and −1.037314721j. It reduces to negative j times the reciprocal of tanh(b) on this axis.

On the real axis, cotangent has poles at integer multiples of pi where sine is zero. This mathematical statement does not establish the application’s exact error at zero or its treatment of a finite approximation to PI(). Those native boundary outcomes remain unverified.

The official 4−3i example has coefficients approximately 0.00490118239430447 and 0.999266927805902, corroborated by the same equation. The source identifies OpenDocument 1.2 membership, which is separate from the unknown first Collabora release. Invalid strings, mixed suffixes, coercions and extreme numerical limits lack a complete dedicated error table.

• Collabora Office 26.04: IMCOT.
• 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.