IMCOT Function (Calligra Sheets)

• Introduced: First release not established; the name is present in Calligra 2.4.0 source.
• Supported in: Calligra Sheets 26.08.2, with no retirement established.
• Scope: Desktop Sheets with the Engineering module. Examples use English semicolon-separated formulas.
• Checked: October 14, 2026. Formulas were executed through the official 25.04.2 engine library and checked against source and independent mathematics. This is not GUI-cell or workbook-import evidence; 26.08.2 was source-checked, not executed.

IMCOT returns cot(z) = cos(z)/sin(z). It is the reciprocal of tangent where both expressions are defined, not an inverse-angle arctangent. Its mathematical poles occur at real integer multiples of π. Function help.

=IMCOT(complexValue)

Provide exactly one complex value. Both components can be constructed explicitly with COMPLEX(real;imaginary). Numeric values are purely real, and the radian convention applies. Registration and implementation, with versioned help.

Results are shown as (real,imaginary) component pairs, rounded to twelve decimal places, not a literal cell format. Tiny or very large values use thirteen significant digits in scientific notation. A component rounded to zero is shown as 0; the stored value may still contain a tiny residual or signed zero. NaN means not-a-number; infinity and NaN are not finite results.

For z = i, cot(i) = −i coth(1), approximately 0−1.313035285499i. Compare the sign with tan(i), which is positive imaginary: the reciprocal of a purely positive imaginary number is negative imaginary.

For a worksheet with numeric components in A2:B2, use =IMCOT(COMPLEX(A2;B2)). Retain the divisor-related domain restriction when the inputs come from another calculation.

The executed product IMCOT(z)×IMTAN(z), formed with IMPRODUCT at z = 0.5+0.25i, returned (1,0). The reciprocal identity only applies where both functions are defined; it cannot resolve a pole by multiplying an undefined value by zero.

Using sin(a+bi) and cos(a+bi), the quotient can be written [sin(2a)−i sinh(2b)]/[cosh(2b)−cos(2a)] when the denominator is nonzero. This makes the sign of the imaginary part and the zero-denominator restriction explicit.

The exact advanced-check formula was:

=IMPRODUCT(IMCOT(COMPLEX(0.5;0.25));IMTAN(COMPLEX(0.5;0.25)))

At exact numeric zero, the tested engine returned (+Infinity,NaN) with its error flag unset. This is not a finite complex result and is not evidence of the worksheet’s displayed error text. The source divides cosine by sine without a worksheet-specific pole guard.

Invalid and empty text also became zero, reaching the same nonfinite result. IMCOT(PI()) was a large finite negative value because rounded PI() is not exact π. Validate both input parsing and denominator size.

The complex conversion helper explains the text and Boolean cases above. The inspected Engineering module and complex converter are byte-identical between 25.04.2 and 26.08.2. That source comparison does not establish every locale, import path or extreme-value case.

Use COMPLEX to construct values from numeric components, IMABS for magnitude, and IMARGUMENT for principal phase.