IMSIN Function (LibreOffice Calc)

IMSIN calculates the sine of a complex number such as "4-3i". The result is a complex-number text string. It is not the same data type as the numerical result from SIN when the input has no imaginary component.

For z=a+bi, the mathematical identity is sin(z)=sin(a)cosh(b)+i cos(a)sinh(b). LibreOffice handles this calculation and the complex-number formatting directly. The real component uses radians.

=IMSIN(Complex_number)

Complex_number — Required. One complex-number expression, a reference to a cell containing it, a formula returning one, or a real numeric value. Complex numbers are represented as text such as "4-3i", "3+4j", or values created with COMPLEX.

IMSIN has one argument, not an optional second parameter. The real and imaginary coefficients use the suffix i or j. Numeric real-only arguments are permitted, although the function returns text. The English-US examples use a period as the decimal separator and semicolons between function arguments (only the nested COMPLEX and other multiargument formulas need separators); other locales or customized Calc formula separators may differ. Use Calc’s formula editor if an imported formula produces a separator error. LibreOffice’s official Help describes the complex-input text representation and textual output for complex trigonometric functions; the legacy analysis-function page covers IMSQRT.

Create this small Calc input table (enter A2 as plain text):

On a narrow screen, scroll this table sideways to see every column.

In D2 enter:

=IMSIN(A2)

Expected and observed (LibreOffice Calc 25.2.3.2): -7.61923172032141+6.548120040911i. It matches the official LibreOffice example with the literal input:

=IMSIN("4-3i")

The real sine example:

=IMSIN(2)

Expected and observed: 0.909297426825682 (as a text string). By comparison, ordinary SIN(2) is numeric. Zero returns a zero text result:

=IMSIN("0+0i")

Expected and observed: 0.

Use numeric values B2=4 and C2=-3 to build the input using the separately documented COMPLEX function:

=IMSIN(COMPLEX(B2;C2))

Expected and observed: -7.61923172032141+6.548120040911i. This workflow avoids concatenating numbers with hand-built plus/minus signs. For a sign-symmetry sanity check, complex sine is odd: sin(-z)=-sin(z).

=IMSUM(IMSIN("1+2i");IMSIN("-1-2i"))

Expected and observed in Calc: 0. This verifies the equality on that particular input; it is not a guarantee that floating-point serialization is exact for every complex input.

• Malformed input: =IMSIN("not-a-number") returned Err:502 in Calc 25.2.3.2. Ensure an i/j suffix, correct sign, and a numeric coefficient rather than arbitrary text.
• Normal sine versus complex sine: SIN(2) is numeric while IMSIN(2) returns a string. Use IMREAL(IMSIN(A2)) if you only need its real coefficient.
• Imaginary part appears missing: A zero component is omitted by design; it does not imply the function ignored the input.
• Input from CSV fails: Import text literally; if Calc transforms a string or strips the suffix, inspect the actual cell content and force text entry if needed. Avoid mixing the imaginary-unit suffix with a variable name.
• Radians versus degrees: The real part of the argument is in radians. Convert degree-based angles with RADIANS before feeding them as real coefficients.
• String results versus number formatting: Formatting the result cell as a decimal number will not turn a complex string into a scalar; extract a coefficient first when required.

• LibreOffice Calc: The official 26.8 Help function catalogue lists this function. Native formula execution below was performed on LibreOffice Calc 25.2.3.2 using the actual UNO spreadsheet engine, not by evaluating the expression in Python. The targeted Help page can display a different version banner in cached views; no function-introduction version is asserted without explicit release evidence.
• Excel: Microsoft’s current function inventory lists this function under Engineering. Formula argument separators and text formatting may differ with locale and software versions; no Excel formula was executed for this draft.
• Google Sheets: Google’s published function inventory also lists this function. Text serialization, locale separators, and very small rounding differences should be verified after import; no Google Sheets formula was executed.
• ODF: The LibreOffice function Help identifies these complex trigonometric functions as part of OpenDocument 1.2; the IMSQRT analysis-function reference supplies its syntax and example. Do not infer that every LibreOffice version or web/mobile implementation has been checked.

The following target slugs and source files were confirmed in the archived 2026-10-10 owner-source bundle; a current live-site link check is still required before publishing:

• COMPLEX — create a complex number from real and imaginary coefficients.
• IMREAL and IMAGINARY — inspect individual components.
• IMPRODUCT and IMSUM — combine complex values.

• LibreOffice Calc official function help — checked 2026-10-11; purpose, exact signature, input/output rules, and published examples.
• LibreOffice Calc Add-in/analysis functions — checked 2026-10-11; category listing and complex/IMSQRT functions.
• Microsoft Excel official function inventory — checked 2026-10-11; cross-software existence only.
• Google Sheets official function inventory — checked 2026-10-11; cross-software existence only.

Selected example formulas were run in LibreOffice Calc 25.2.3.2 on Linux on October 12, 2026. The official Help may cover a newer version. Tests of selected formulas do not certify every locale, interactive array operation or file round trip. View the example-check record.

Official IMSIN reference · Editorial standards