IMCOSH Function (OpenOffice Calc)

• Introduced: First release not established; the pinned 4.1.16 source confirms current-release presence.
• Supported in: Apache OpenOffice 4.1.16; this identifies a verified release, not a final supported version.
• Scope: Desktop Calc with its Analysis add-in, English function names and semicolon-separated formulas.
• Checked: October 14, 2026. Eight reference formulas and the listed diagnostics were recalculated from generated native-ODF input in 4.1.16 on Linux x86-64, Build 9816. Source and independent reference calculations were also checked.

IMCOSH returns hyperbolic cosine for a parsed complex value. It is different from IMCOS: the hyperbolic operation applies to the real component in its component formula, while ordinary sine and cosine handle the imaginary component. For z=a+bi, the independent component formula is cosh(a+bi)=cosh(a)cos(b)+i sinh(a)sin(b). Release entry.

=IMCOSH(ComplexNumber)

Exactly one complex-number argument is required. The add-in parses pure real forms and complex strings with lowercase i or j. Its strict parser rejects nonempty malformed text and empty strings. The trigonometric angles in the component formulas are in radians, not degrees.

The native column records the saved 4.1.16 results. The native strings are retained exactly. Independent component references are rounded to twelve decimal places, with rounded negative zero shown as zero. A tiny stored residual can therefore appear in the native string beside a reference component rounded to zero. Every successful result below is string-typed, including pure real-looking outputs.

At 1+i the components are approximately 0.833730025131 and +0.988897705763. Compare the positive imaginary sign with complex cosine at the same input. For the pure imaginary input i, cosh(i)=cos(1), approximately 0.540302305868.

For a worksheet, place a validated complex value in A2 and use =IMCOSH(A2). This is an illustrative layout for the tested literal argument. Keeping real and imaginary measurements separately can make unit, sign and parsing mistakes easier to detect.

Hyperbolic cosine is even: cosh(−z)=cosh(z). Conjugating the input conjugates the output. These properties explain the sign pattern across the four quadrant examples.

The identity cosh(z)²−sinh(z)²=1 is an identity of complex values. It is not a difference of squared magnitudes. Another relation is cosh(z)=cos(iz); multiplication by i swaps the component roles and changes one sign. These provide independent checks without interpreting the output as a real probability or bounded cosine.

Zero is valid and returns 1. Hyperbolic cosine can grow rapidly with the magnitude of the real component. Finite mathematical inputs can still overflow the numeric implementation. Current support is verified independently of its unknown first-release date; the older appendix used for IMCOS does not establish IMCOSH history.

These additional formulas were recalculated through the same generated-ODF path. Error displays are retained as errors, even when an ODS numeric attribute stores zero.

The IMCOSH guide for LibreOffice Calc documents that product’s own syntax and tested behavior. A shared function name does not guarantee the same argument conversion, text parsing, branch or precision rules.

• Function-specific release entry
• Complex algorithm or collection helper
• Strict complex-string parser
• Finite-output string formatter

The saved ODS retained every tested formula identity. A deliberately stale SUM cache changed from 999999 to 3, and an uncached SUM returned 7 after hard recalculation. The application reported “Not all attributes could be read” on loading the generated input. All tested identities and input text survived, but preservation of every style attribute was not established. Native evidence covers the eight reference formulas and listed diagnostics only; it does not establish XLSX-import or manual-entry behavior. Other explanatory compositions are independent mathematical checks; other releases, locales and extreme-value behavior were not established by this run.