IMTAN

What it does

IMTAN(inumber)

IMTAN(inumber) returns the complex tangent. Real and imaginary coefficients use radians where a circular angle is involved. The real-axis kernel has a separate circular-trigonometric domain check.

Try it

=IMTAN("i") gives about "0.761594155955765i". The doubled-angle formula reduces mathematically to i*tanh(1) on this axis. =IMTAN("0") returns text zero.

Quirks

The result is complex text. A malformed input gives #NUM! in the current parser; a logical input gives #VALUE! in the wrapper. The non-real formula has a denominator made from circular and hyperbolic terms, so overflow and a zero denominator need explicit handling.

Exactly real input uses the scalar tangent and its circular-domain check. The real-axis IMCOT companion has a separate reciprocal and boundary rule; treating both as a generic quotient of formatted IMSIN and IMCOS loses that distinction.

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)/(cos(2*a)+cosh(2*b)) + i*sinh(2*b)/(cos(2*a)+cosh(2*b)). 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

50 imtan "IMTAN" (1, 1) [V "inumber"] |s, a, sv| { unary_complex(s, a, |z| z.tan()) }

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

IMCOT is the cotangent companion. IMSIN and IMCOS expose the circular pair, and TAN accepts a real angle.

Named variants

No named variants are recorded yet.