IMSIN Function (OpenOffice Calc)

• Introduced: First release not established; documented by OpenOffice.org 3.3.
• 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.

IMSIN returns sine for a parsed complex argument. It is a complex extension of ordinary sine, so it need not be real or bounded in magnitude by 1. The result is complex-number text. For z=a+bi, the independent component formula is sin(a+bi)=sin(a)cosh(b)+i cos(a)sinh(b). Release entry.

=IMSIN(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 result has components about 1.298457581416 and +0.634963914785. The real component exceeding 1 is valid. For i alone, sin(i)=i sinh(1), which is purely imaginary. The argument’s trigonometric components use radians.

For a worksheet, place a validated complex value in A2 and use =IMSIN(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.

Sine is odd: sin(−z)=−sin(z). It also respects conjugation. The quadrant rows let you check those properties without relying on a single example.

The identity sin(z)²+cos(z)²=1 holds for complex values. Using squared magnitudes instead would produce cosh(2b) for z=a+bi, which generally differs from 1. Another useful relation is sin(iz)=i sinh(z); it connects the ordinary and hyperbolic function families.

Zero is valid and returns the string 0. Complex sine has no finite mathematical poles, but hyperbolic growth from a large imaginary component can overflow finite-precision intermediates. The shared parser rejects malformed or empty strings, and the formatter rejects nonfinite components. The modest examples establish the displayed cases only.

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 IMSIN 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.