IMSINH Function (LibreOffice Calc)

IMSINH returns the hyperbolic sine of a complex number as a complex-number text result. In native LibreOffice Calc 25.2.3.2, =IMSINH("4-3i") returned -27.0168132580039-3.85373803791938i.

=IMSINH(Complex_number)

Complex_number (required): a string in complex notation a+bi or a+bj, a cell reference to such text, a COMPLEX(real;imaginary) expression, or a real numeric value. There are no optional arguments. Output type is string, including for purely real input.

Version and locale: The displayed current English online documentation says LibreOffice 26.8 Help. All native examples below were executed in desktop LibreOffice Calc 25.2.3.2, not the documented 26.8 runtime. English Calc formula examples separate different function arguments with a semicolon (;); complex-number coefficients within one quoted string are not separate arguments. Actual separators and decimal marks can follow your locale. The documented IMCOSH/IMSINH entries specifically say the functions are available since LibreOffice 3.6; other two functions are confirmed in the Help and tested in 25.2 but no undocumented first-version claim is made.

For z=x+iy, sinh(z)=sinh(x)cos(y)+i cosh(x)sin(y). This differs from the ordinary circular complex sine function IMSIN. Hyperbolic sine is an odd function: sinh(-z)=-sinh(z). If a part of the complex result is zero, Calc omits that part when displaying the complex-number text.

Enter complex text 4-3i into A3; numeric 3 and 4 into B2 and C2. Native =IMSINH(A3) returned -27.0168132580039-3.85373803791938i. Native =IMSINH(COMPLEX(B2;C2)) returned -6.548120040911-7.61923172032141i. For A4 containing 1+j, =IMSINH(A4) returned 0.634963914784736+1.29845758141598j.

To recreate the result, enter the indicated literal complex values as cell text (without a leading equals sign), insert the formula into a different empty cell, and allow Calc to recalculate. Values listed below reflect the actual observed Calc results rather than screenshots or hypothetical applications.

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

Check the identity cosh²(z)-sinh²(z)=1 using =IMSUB(IMPRODUCT(IMCOSH("1+i");IMCOSH("1+i"));IMPRODUCT(IMSINH("1+i");IMSINH("1+i"))). Native Calc yielded 1.00000000000001, rather than exact text "1"; this reflects floating-point rounding in a chain of complex operations. For numeric tolerance testing, pull out the real and imaginary coefficients and compare within a chosen tolerance.

=IMSINH("oops") and =IMSINH("3+4k") both returned Err:502 in this Calc test. Text that does not follow the accepted i/j notation is invalid. If a numeric result seems plausible but cannot be summed, remember it remains complex-number text.

Type and precision: Use SINH for a real numeric result. IMSINH is appropriate for input that may have a nonzero imaginary part. Floating-point computations should generally be checked by numeric tolerance rather than string exact-match. ODF/Excel/Sheets file-format round-trips can affect syntax, prefixes or formatting; export/import behaviour was not tested here.

Need a numeric scalar? =ISTEXT(IMSINH(2)) returned TRUE in native Calc; use IMREAL(IMSINH(2)) to extract a number or call numeric SINH(2) directly for real-only work. Unexpected sign? Changing z to -z changes the sign of the result; keep the real and imaginary coefficients in the intended quadrant. Wrong suffix? Use only i or j in valid complex text, or build it with COMPLEX. Different final digits? Expect floating-point rounding, particularly in chained identities.

If you cannot reproduce the result, first confirm the exact formula in the formula bar, check the cell’s source value, inspect decimal and list separators for your locale, and compare the software version. Use simple examples before adding other nested formulas.

LibreOffice Help identifies IMSINH as available since LibreOffice 3.6 and documents it in ODF 1.2. Excel has documented IMSINH (Excel 2013 onward in the category reference); Google Sheets lists IMSINH. Their argument-separator locales and returned error displays may differ. This batch did not run Excel or Sheets formulas. See official cross-software references below; no native Excel or Google Sheets tests were performed.

• IMCOSH function in LibreOffice Calc
• IMSIN function in LibreOffice Calc
• IMCOS function in LibreOffice Calc
• IMPRODUCT function in LibreOffice Calc
• IMSUB function in LibreOffice Calc
• IMREAL function in LibreOffice Calc
• COMPLEX function in LibreOffice Calc

• LibreOffice official function page: Documentation for IMSINH — accessed 2026-10-11, current display LibreOffice 26.8 Help. Supports named function, purpose, syntax, argument form, and its documented examples.
• LibreOffice official analysis-functions list: Add-in Functions, Part Two — accessed 2026-10-11. Explains COMPLEX, IMARGUMENT, IMLOG2 and related engineering functions.
• Microsoft: Engineering functions reference — consulted 2026-10-11 for equivalent Excel function availability; no Excel execution claimed.
• Google: Sheets function list — consulted 2026-10-11 for function availability; no Sheets execution claimed.
• Native evidence: The accompanying native_calc_results.json and native_calc_test.py record observed Calc output, numeric/error types and independent Python math comparisons. 34/34 assertions passed across this four-page batch and 8 additional error observations were recorded; not every explanatory derivative formula was executed.

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 IMSINH reference · Editorial standards