IMSINH

What it does

IMSINH(inumber)

IMSINH(inumber) returns the complex hyperbolic sine. Real and imaginary coefficients use radians where a circular angle is involved. A real-only input has a real-only result; an imaginary input relates to ordinary sine.

Try it

=IMSINH("i") gives about "0.841470984807897i". For a pure imaginary input the real component vanishes and the imaginary component is ordinary sine. =IMSINH("0") returns text zero.

Quirks

Complex text uses lowercase i or j; the result is text. The current parser gives #NUM! for malformed text and the wrapper gives #VALUE! for a logical input.

On the real axis the direct function checks EXP's overflow domain and keeps the imaginary component zero without evaluating an infinity-times-zero product. Its reciprocal companion IMCSCH has a wider runtime computation. Large real-axis inputs need a separate comparison from ordinary non-real pairs.

How to implement

Parse the two coefficients and suffix before doing arithmetic; use the common complex formatter afterward. Retain suffix consistency, suppress a zero component and omit the coefficient one before the imaginary unit. Formatting and parsing have their own fifteen-significant-digit rules, so testing only the algebra misses observable behaviour.

For z=a+bi, the mathematical component formula is sinh(a)*cos(b) + i*cosh(a)*sin(b). The current real-axis direct hyperbolic route enforces the exponential overflow domain and avoids an infinity-times-zero imaginary component. The formula is a derivation aid; the named runtime leaves and stores in the current source define its implementation candidate. Validate text output as well as numeric components, and keep unmeasured rounding stages open.

Rust code

48 imsinh "IMSINH" (1, 1) [V "inumber"] |s, a, sv| { unary_complex(s, a, |z| { z.check_real_hyperbolic_domain()?; Ok(z.sinh()) }) }

No implementation has been published with a Handbook test suite for this function.

Version differences

The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.

The record contains no same-input comparison between these environments. Reading different inputs on different builds does not establish either a version change or cross-build agreement.

Recorded environments and comparison details.

Alternatives

IMCSCH is the reciprocal hyperbolic function. IMCOS and IMSIN are the circular companions. COMPLEX constructs an input from two numeric coefficients.

Named variants

No named variants are recorded yet.