IMSECH 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.

IMSECH returns sech(z) = 1/cosh(z). It is the reciprocal of hyperbolic cosine, not an inverse hyperbolic function. Mathematical poles occur at z = i(π/2+kπ) for integer k. Function help.

=IMSECH(complexValue)

Exactly one complex argument is accepted. The examples construct real and imaginary components with COMPLEX. Numeric arguments have zero imaginary part; the imaginary-axis angular component uses 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.

At z = i, sech(i)=sec(1), approximately 1.850815717681. A value above 1 is valid for this complex input, even though real sech(a) is at most 1. The imaginary-axis identity changes the relevant behavior.

With numeric components in A2:B2, use =IMSECH(COMPLEX(A2;B2)). Do not reciprocate only the real part of IMCOSH when its imaginary part is nonzero.

For z = 0.5+0.25i, the executed product IMSECH(z)×IMCOSH(z) returned real component 1 with an imaginary residual about −6.776263578034E−21. This verifies the reciprocal relation at that ordinary input, allowing for finite precision.

Sech is even because cosh is even. For real b, sech(ib)=sec(b); consequently a purely imaginary input can produce a large real output near a cosine zero, unlike the bounded real-axis function.

The exact advanced-check formula was:

=IMPRODUCT(IMSECH(COMPLEX(0.5;0.25));IMCOSH(COMPLEX(0.5;0.25)))

IMSECH(COMPLEX(0;PI()/2)) returned a large finite real component near 1.633123935320E16. It reflects the rounded angle’s nonzero cosine; exact sech(iπ/2) is undefined. Reciprocals amplify a small denominator and any uncertainty in it.

Invalid and empty text converted to zero, so their results were 1 with no error flag. Validate strings separately. The component observations do not establish cell-display error handling or extreme-parameter accuracy.

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.