IMSIN 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.

IMSIN returns the sine of a complex value. For z = a+bi, sin(z) = sin(a)cosh(b) + i cos(a)sinh(b). The real component a is an angle in radians. Unlike real sine, complex sine is not bounded in magnitude by 1. Function help.

=IMSIN(complexValue)

Exactly one complex value is required. A COMPLEX(real;imaginary) expression makes both input components explicit. Numeric values are treated as purely real; supported complex text can also be parsed. 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 the purely imaginary input i, the table gives imaginary component approximately 1.175201193644 and real component zero. This is sin(i) = i sinh(1), so a magnitude above 1 is expected. It is not a real-angle sine error.

To keep components in a worksheet, put real part 0 in A2 and imaginary part 1 in B2, then use =IMSIN(COMPLEX(A2;B2)). This cell layout mirrors the explicit component constructor in the executed reference row.

The identity sin²(z)+cos²(z)=1 holds for complex z as well as real angles. For z = 0.5+0.25i, the executed advanced check squared IMSIN and IMCOS with IMPOWER and added them with IMSUM; it returned components (1,0). Use complex arithmetic functions for this check rather than squaring formatted text.

Sine is odd: sin(−z)=−sin(z). Conjugating an input conjugates its sine. The reference rows with opposite signs make these component relations visible.

The exact advanced-check formula was:

=IMSUM(IMPOWER(IMSIN(COMPLEX(0.5;0.25));2);IMPOWER(IMCOS(COMPLEX(0.5;0.25));2))

The versioned help prints IMSIN(“1.2”) as approximately −0.536573. The dedicated engine check below returned approximately 0.932039085967, agreeing with sin(1.2 radians). The help value must not be used as the expected answer.

Invalid text and an empty string converted to complex zero in these engine cases, producing zero rather than an error. Validate imported text before relying on that result. IMSIN(PI()) retained a tiny nonzero component because the input PI() is rounded, not exact mathematical π.

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.