IMCOT

What it does

IMCOT(inumber)

IMCOT(inumber) returns the complex cotangent. Real and imaginary coefficients use radians where a circular angle is involved. The denominator vanishes at zero; the current function gives #NUM! there.

Try it

=IMCOT("i") gives about "-1.31303528549933i". On this axis it is mathematically -i*coth(1). =IMCOT("0") has a zero denominator and the current function returns #NUM!.

Quirks

The result is complex text and lowercase i or j is supported. Malformed complex text gives #NUM! in the current parser; a logical argument gives #VALUE! in the wrapper. Zero is a pole.

For exactly real input the current helper takes a stored reciprocal of scalar tangent. It returns text zero at the finite circular-domain boundary where IMTAN gives #NUM!. For non-real inputs it uses a doubled-angle formula, whose denominator can vanish or overflow. These are separate compatibility branches.

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 sin(2*a)/(cosh(2*b)-cos(2*a)) - i*sinh(2*b)/(cosh(2*b)-cos(2*a)). Use the doubled-angle graph for non-real input. On the real axis the current tangent uses its scalar tangent leaf, while cotangent uses one stored reciprocal; their domain-boundary outputs are not identical. 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

38 imcot "IMCOT" (1, 1) [V "inumber"] |s, a, sv| { unary_complex(s, a, |z| z.cot()) }

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

IMTAN returns tangent. IMDIV handles general complex division, while COT accepts a real angle.

Named variants

No named variants are recorded yet.