IMSINH 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.

IMSINH returns sinh(z) = [exp(z)−exp(−z)]/2. For z = a+bi, its components are sinh(a)cos(b) and cosh(a)sin(b). The imaginary component b is used as a radian angle in this identity; this is not ordinary complex sine. Function help.

=IMSINH(complexValue)

Exactly one complex argument is required. Use COMPLEX(real;imaginary) to construct explicit components. Pure real numeric inputs are accepted; recognized complex text is converted by the shared helper. 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, sinh(i)=i sin(1), approximately 0+0.841470984808i. In contrast, sinh(1) is approximately 1.175201193644 on the real axis. Swapping real and imaginary input positions changes both the magnitude relationship and output direction.

With A2=0 and B2=1, =IMSINH(COMPLEX(A2;B2)) expresses the imaginary-axis example directly.

The identity cosh²(z)−sinh²(z)=1 holds for complex inputs. At z = 0.5+0.25i, the executed difference of the IMPOWER squares had real component 1.00000000000000000022 and imaginary component about 2.710505431214E−20. These small residuals are retained rather than described as exact arithmetic.

Hyperbolic sine is odd, and conjugating its input conjugates the result. Large real parts can make its magnitude grow rapidly, unlike real sine’s bounded behavior.

The exact advanced-check formula was:

=IMSUB(IMPOWER(IMCOSH(COMPLEX(0.5;0.25));2);IMPOWER(IMSINH(COMPLEX(0.5;0.25));2))

Invalid and empty text became complex zero, giving zero hyperbolic sine without an error flag. A successful zero therefore does not prove that the input string was valid.

IMSINH(COMPLEX(0;PI())) had a tiny imaginary residual near 1.224646799147E−16. Mathematical sinh(iπ) is zero; the observed remainder comes from the rounded π supplied to the function. Other large-argument or overflow cases are outside these tests.

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.