IMSINH 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.

IMSINH returns the hyperbolic sine of a parsed complex number. It combines hyperbolic functions of the real component with trigonometric functions of the imaginary component. It is different from IMSIN and from an inverse hyperbolic sine operation. For z=a+bi, the independent component formula is sinh(a+bi)=sinh(a)cos(b)+i cosh(a)sin(b). Release entry.

=IMSINH(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.

For 1+i, the components are approximately 0.634963914785 and +1.298457581416. For the pure imaginary input i, sinh(i)=i sin(1), while the real input 1 gives the ordinary positive real sinh(1). These two cases help distinguish which component controls exponential growth.

For a worksheet, place a validated complex value in A2 and use =IMSINH(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 sine is odd and respects conjugation. The identity cosh(z)²−sinh(z)²=1 is an identity of complex values, so checking it requires complex multiplication rather than squaring magnitudes.

The relation sinh(z)=−i sin(iz) follows from the ordinary sine identity. With a real positive input, hyperbolic sine grows rapidly; with a pure imaginary input, it reduces to a bounded sine multiplied by i. These different directions explain why a single real-domain intuition is insufficient.

Zero is accepted and returns 0. There are no finite mathematical poles, but finite-precision overflow is possible for sufficiently large real components. Invalid text, empty strings and excess arguments are distinct diagnostic errors. Do not interpret a returned string that looks numeric as proof of ordinary real-cell arithmetic.

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 IMSINH 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.