IMCOSH 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.

IMCOSH returns cosh(z) = [exp(z)+exp(−z)]/2. For z = a+bi, the real component is cosh(a)cos(b) and the imaginary component is sinh(a)sin(b). It should not be confused with ordinary complex cosine, which has a different imaginary sign and component roles. Function help.

=IMCOSH(complexValue)

One complex argument is required. A COMPLEX(real;imaginary) constructor makes the numerical parts unambiguous. Pure real numbers and recognized complex strings are also accepted by the converter. 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.

At z = i, cosh(i)=cos(1), approximately 0.540302305868. This is a real result below 1, unlike real cosh(1), approximately 1.543080634815. The real-axis lower bound of 1 does not extend to arbitrary complex arguments.

The worksheet formula =IMCOSH(COMPLEX(A2;B2)) keeps the distinction visible when the two components are entered in separate numeric cells.

Hyperbolic cosine is even: cosh(−z)=cosh(z). For z = 0.5+0.25i, the executed complex difference of the two values returned (0,0). Conjugation symmetry also explains the opposite imaginary signs in paired reference rows.

The identity cosh²(z)−sinh²(z)=1 continues into the complex plane. On the imaginary axis it reduces to cos²(b)+sin²(b)=1 because squaring i sin(b) contributes a minus sign.

The exact advanced-check formula was:

=IMSUB(IMCOSH(COMPLEX(0.5;0.25));IMCOSH(IMSUB(0;COMPLEX(0.5;0.25))))

Invalid or empty text became complex zero in the tested conversion path, so its hyperbolic cosine was 1. That plausible answer should not replace validation of imported values.

IMCOSH(COMPLEX(0;PI()/2)) returned a tiny real component near 6.123233995737E−17 rather than mathematical zero. The angle is a rounded π/2. This matters when a later calculation reciprocates the value and amplifies the small residual.

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.