IMCSCH Function (LibreOffice Calc)

IMCSCH calculates the hyperbolic cosecant of a complex number z. In mathematics, csch(z) = 1 / sinh(z). For a quick numeric example, enter:

=IMCSCH(2)

Observed in LibreOffice Calc 25.2.3.2: the displayed result was 0.275720564771783. Even though this answer looks numeric, IMCSCH returns text: =ISTEXT(IMCSCH(2)) displayed TRUE, while =ISNUMBER(IMCSCH(2)) displayed FALSE in native testing. LibreOffice explicitly documents the string return type.

IMCSCH(Complex_number)

Complex_number — Required. A complex-number string such as "1+2i", "4-3i", or "1+2j"; a reference to a cell containing such text; a result of COMPLEX; or a real numeric argument such as 2 when the imaginary part is zero.

One mandatory argument; no optional arguments or defaults. The imaginary unit must be i or j. The official IMCSCH reference documents string input and allows numeric real input. The function has been available since LibreOffice 3.6. The reference displayed LibreOffice 26.8 Help when checked October 11, 2026; the current category index displayed LibreOffice 26.8 Help. All executed Calc examples below were run on Linux with version 25.2.3.2; neither Windows nor macOS was tested.

Locale note: The examples use English function names. This function takes only one argument, so no argument separator appears in its direct call; nested Calc functions use the semicolon separator, as in =COMPLEX(3;4;"i"). Other locale formula settings and complex-number decimal notation were not natively tested. Literal complex strings are enclosed in double quotes and are not spreadsheet references. ODF interoperability and the function’s introduction version are documented in LibreOffice Help.

Create a fresh LibreOffice Calc sheet. Type the inputs in column A exactly as shown. Complex inputs can be stored as text; enter the letter i or j literally. In the corresponding B cells, enter the formula. The expected numbers below were observed in the native test either using the displayed literal formula or, where explicitly indicated, using the A2 reference.

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

The A2 reference calculation was executed in Calc as written, with A2 holding the string 1+2i. The other four rows reproduce executed literal-formula calls. No screenshot is claimed. Decimal output is displayed at Calc’s tested precision; minor rounding differences across builds are possible. The sample result for 4-3i also matches the vendor’s documented example.

Why the sign and suffix matter

Hyperbolic cosecant is odd: csch(-2) = -csch(2); the real-input test returned the same magnitude with a negative sign. The 1+2j formula produced the j suffix in the returned complex string, whereas 1+2i produced i. This is a formatting/notation distinction, not a separate function or page. If your data contain a mix of i and j, standardize the inputs before joining or comparing text values.

Suppose your source table has numeric real parts in B2 and imaginary parts in C2. For B2 = 3 and C2 = 4, enter:

=IMCSCH(COMPLEX(B2;C2;"i"))

Expected from native Calc testing of the equivalent constant-input formula: -0.0648774713706355+0.0754898329158637i. The directly executed test was =IMCSCH(COMPLEX(3;4;"i")), not the exact B2/C2 reference variant. The reference variant uses the same documented arguments; verify it with your own cell values. See the official COMPLEX syntax: COMPLEX(RealNum; INum [; Suffix]). Select the suffix deliberately when sharing workbooks.

For z = 1+2i, the reciprocal identity is csch(z) = 1 / sinh(z). An independent worksheet check is:

=IMPRODUCT(IMCSCH("1+2i");IMSINH("1+2i"))

Native observed: 1+8.88178419700125e-16i. That is approximately 1: the tiny imaginary residue is floating-point roundoff, not a mathematically meaningful additional imaginary component. This identity only holds where the denominator is nonzero. The test passed an independent Python cmath check to absolute tolerance 1e-11 and was executed in LibreOffice Calc 25.2.3.2.

Since IMCSCH produces text, derive numeric real and imaginary columns explicitly:

=IMREAL(IMCSCH("1+2i"))
=IMAGINARY(IMCSCH("1+2i"))

Native observed numeric components: -0.221500930850509 and -0.6354937992539 respectively. These two IMREAL/IMAGINARY formulas were executed; they return numeric components suitable for charts or further numeric formulas. For engineering work, preserve the original complex string and add calculated component columns rather than treating IMCSCH output as a normal decimal number. See Calc’s IMREAL and IMAGINARY documentation.

Practical use case: a complex response table

For each complex measurement z in a model, keep input strings in a Complex Input column, compute the hyperbolic cosecant in a second column, and extract numeric real/imaginary parts for plotting. For a complex-input model that produces a sinh(z) response, multiply its reciprocal from IMCSCH by the original response to check it is approximately 1 away from singularities. The result changes sign when the real input changes from 2 to -2 (odd function). Avoid interpreting those values as real-world measurements without checking the underlying physical model and units. This illustrates a spreadsheet procedure; it does not imply a validated scientific application.

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

The zero input and malformed strings were observed as Calc Err:502. Near poles a floating-point result can be huge or unstable; this risk follows from the mathematical denominator and was not exhaustively sampled. Very large real components can magnify rounding and overflow concerns in hyperbolic functions. Neither a full error-domain survey nor operating-system portability testing was performed. LibreOffice Help describes the input and result types.

1. Check the single argument. =IMCSCH("1+2i") is the complete function. For two numeric components, first build a complex value with COMPLEX(real; imaginary; "i") and pass that single result.
2. Check the imaginary suffix and quotes. "1+2k" is invalid in the native test. Valid string examples end with i or j, and constants containing + or - should be quoted.
3. Check the reference cell type. If you intended A2 to contain 1+2i, verify A2 actually holds that text, not a blank cell or a display format applied to another value. The native =IMCSCH(A2) test with A2 = 1+2i produced -0.221500930850509-0.6354937992539i.
4. Know the mathematical domain. The denominator sinh(z) must not be zero. In exact complex mathematics, zeros occur at z = nπi for integers n; z = 0 is the simplest singularity. Avoid blindly suppressing spreadsheet errors near poles.
5. Confirm the return type. ISTEXT confirmed text output; if you need numeric values use IMREAL and IMAGINARY or another explicitly documented complex-number operation.
6. Revisit locale and spreadsheet application. Error codes, number formatting, decimal separators, and text coercion differ across installations. This guide’s detailed output is from Calc 25.2.3.2 on Linux, not a guarantee for every platform.

Microsoft documents the same IMCSCH spelling and one required complex-number argument for supported Excel editions. The Excel result is also complex-number text (x+yi or x+yj), and Excel documents #NUM! for malformed complex text and #VALUE! for a logical input; these Excel-specific errors must not be confused with the Calc 25.2.3.2 observations above. Microsoft’s official IMCSCH documentation lists Excel for Microsoft 365, Excel 2024/2021, Excel 2019, Excel 2016 and Mac variants where specified. Excel was not natively executed in the recorded checks. Support in Google Sheets and alternative spreadsheet engines was not independently verified, so equivalent names and behaviour should not be assumed.

• IMSINH — the denominator function in the reciprocal identity.
• IMCSCH — hyperbolic cosecant.
• IMSECH — hyperbolic secant.
• COMPLEX — construct complex strings from coefficients.
• IMREAL — extract a numeric real part.
• IMAGINARY — extract a numeric imaginary part.

• Official LibreOffice function page (checked October 11, 2026): IMCSCH. The page displayed LibreOffice 26.8 Help. Supports purpose, required syntax, i/j notation, version 3.6 availability, string result type, and official example.
• Official LibreOffice category/function overview (checked October 11, 2026): Add-in engineering functions, displayed 26.8 Help. Supports COMPLEX, IMREAL/IMAGINARY and related functions.
• Excel vendor comparison (checked October 11, 2026): Microsoft IMCSCH. Documentation checked; Excel not executed.
• Executed test: LibreOffice Calc 25.2.3.2 on Linux, isolated headless UNO spreadsheet. Source formulas, native outputs, error codes and ISTEXT/ISNUMBER checks are recorded in research/native-test-results.json. Independent Python cmath expected-value assertions are in research/native-assertions.json (34/34 assertions passed across the two functions, with explicit error expectations and tolerance).

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 IMCSCH reference · Editorial standards