IMSINH in Collabora Office: Rebuild Complex Hyperbolic Sine from Exponential Differences

• Introduced: the original Collabora release and launch date are not established by the reviewed sources.
• Availability: documented in Collabora Office 26.04 desktop help.
• Platform scope: online and mobile deployment support is not inferred from the desktop documentation.
• Checked: October 14, 2026. Function-specific documentation and independent controls; no native Collabora execution.

=IMSINH(Complex_number)

The Collabora reference accepts a+bi or a+bj strings and also allows a numeric value when the input is purely real. It explicitly describes every output as a string representing a complex number, with a zero component omitted.

Its numeric control =IMSINH(2) returns approximately 3.62686040784702 as text. Use a real-component extractor if a later calculation needs that real coefficient as a number; a decimal-looking display alone does not change the documented return type.

Format A2:A5 as Text and enter 0.5+0.75j, 2+j, 0.5-0.75j and 2j. Put =IMSINH(A2) in B2, then =IMREAL(B2) in C2 and =IMAGINARY(B2) in D2. Fill down.

The display is rounded to nine decimals. Retain the calculated B values for later checks, and use the numeric C/D coordinates to inspect results.

The first and third rows are conjugates. The second row’s larger real input produces larger hyperbolic factors, while its imaginary input also changes how those factors are distributed between the two output coordinates.

Collabora’s equation states that the real coefficient is sinh(a)×cos(b), and the imaginary coefficient is cosh(a)×sin(b).

For the first row, use:

=SINH(0.5)*COS(0.75)
=COSH(0.5)*SIN(0.75)

The independently expected coefficients match 0.381279635 and 0.768633565. For a cell-driven calculation, substitute IMREAL(A2) and IMAGINARY(A2) for the two coordinates.

IMREAL and IMAGINARY provide the numeric arguments. The ordinary trigonometric functions act on b in radians; the hyperbolic functions act on a. This placement differs from the complex ordinary-sine equation.

Hyperbolic sine is half the difference between the exponentials of z and −z. For the first input, compare:

=IMDIV(IMSUB(IMEXP("0.5+0.75j");IMEXP("-0.5-0.75j"));COMPLEX(2;0;"j"))

The expected coefficients are again 0.381279635 and 0.768633565, rounded. IMEXP supplies the complete complex exponential, and IMSUB subtracts complete quantities before the real divisor two is applied.

The explicit complex divisor avoids assuming an undocumented plain-number coercion by IMDIV. This moderate fixture is suitable for a component tolerance check; subtracting nearly equal exponentials at tiny inputs can behave differently numerically.

Numeric input 2 represents the real-axis quantity 2+0j. Its hyperbolic sine is a real quantity near 3.626860408. Input 2j instead has expected quantity near 0.909297427j, because sinh(bj)=j×sin(b).

Both original magnitudes are two, but the outputs are different. Applying ordinary SINH to the magnitude would discard the direction needed to distinguish them.

Use =IMREAL(IMSINH(2)) to expose the documented real control as a numeric coefficient. The imaginary coefficient extracted from that result is zero; the return representation of IMSINH itself remains the documented string.

Negating both coordinates of 0.5+0.75j gives −0.5−0.75j. Its hyperbolic sine is the negative of the first result, with coefficients approximately −0.381279635 and −0.768633565.

Multiplying the original input by j rotates it to −0.75+0.5j. The identity sin(jz)=j×sinh(z) then has independently expected real coefficient −0.768633565 and imaginary coefficient 0.381279635.

Compare =IMSIN("-0.75+0.5j") with =IMPRODUCT(COMPLEX(0;1;"j");IMSINH(A2)). This checks both coordinate placement and signs, rather than only the magnitude of a result.

IMSIN is the ordinary complex sine; the identity relates two distinct functions rather than making them interchangeable on the same input.

The official 4−3i example gives coefficients approximately −27.0168132580039 and −3.85373803791938, consistent with the same component equation. The reference also identifies OpenDocument 1.2 membership; that is not the first Collabora release.

The dedicated section does not provide a complete invalid-input, mixed-suffix, blank-coercion or numerical-overflow table. All new outputs here are independently calculated expectations, not native application captures. Keep tolerances explicit and do not generalize a moderate example into a universal precision guarantee.

• Collabora Office 26.04: IMSINH.
• Editorial testing standards.

Complete dedicated reference and its equation image reviewed. Examples are independently calculated controls or explicit documented statements, not native application captures. Formulas use English names and semicolon separators.