IMCSC 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.

IMCSC returns csc(z) = 1/sin(z). It is a reciprocal sine, not an arcsine. Mathematical poles occur at real integer multiples of π, including zero. Function help.

=IMCSC(complexValue)

Supply exactly one complex value, such as COMPLEX(real;imaginary). Accepted text is converted to a complex number before calculation. Pure numeric arguments are treated as real and angles use radians. 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, csc(i) = −i/sinh(1), approximately 0−0.850918128239i. The reciprocal changes the sign of the imaginary direction. A magnitude below 1 is valid for this purely imaginary input.

Store the real and imaginary parts in A2:B2 and use =IMCSC(COMPLEX(A2;B2)). Keep the sine-denominator restriction visible if a larger model can move the input near zero.

The executed product IMCSC(z)×IMSIN(z) at z = 0.5+0.25i returned real component 1 and an imaginary residual about −2.710505431214E−20. This is the expected reciprocal identity within numerical precision for a non-pole input.

Cosecant is odd: csc(−z)=−csc(z). Conjugate inputs give conjugate outputs. Neither relation authorizes a value at a pole, because the reciprocal of zero is still undefined.

The exact advanced-check formula was:

=IMPRODUCT(IMCSC(COMPLEX(0.5;0.25));IMSIN(COMPLEX(0.5;0.25)))

At zero, the tested engine returned (+Infinity,NaN) while leaving its error flag unset. This pair is not a usable finite result. The wrapper directly divides one by the complex sine.

Invalid and empty text converted to complex zero and reached the same pole. IMCSC(PI()) instead returned a large positive finite component near 8.165619676598E15, reflecting the rounded angle’s tiny sine. Neither observation establishes literal GUI-cell error formatting.

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.