IMCONJUGATE

What it does

IMCONJUGATE(inumber)

IMCONJUGATE(inumber) reflects a complex number across the real axis, changing the sign of the imaginary coefficient and keeping the real coefficient.

Try it

=IMCONJUGATE("2-3i") returns "2+3i". Multiplying those two inputs mathematically gives thirteen, the square of their modulus.

Quirks

Complex arguments may be real numbers or text such as "2-3i". Use lowercase i or j; operands in one call must agree on the suffix. The current parser rejects malformed complex text with #NUM! and logical values with #VALUE!. A complex result is text, so ordinary worksheet arithmetic does not automatically treat it as a pair of numeric components. A real-only input is unchanged by conjugation.

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.

The arithmetic step is just (a,b) → (a,-b). Normalise signed zero when assembling text. This operation needs no transcendental approximation; nevertheless, conversion to and from complex text can affect long decimal coefficients. Test the textual route separately from a mathematical pair operation.

Rust code

35 imconjugate "IMCONJUGATE" (1, 1) [V "inumber"] |s, a, sv| { unary_complex(s, a, |z| Ok(z.conj())) }

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

IMREAL and IMAGINARY expose the parts; IMABS measures the distance to zero.

Named variants

No named variants are recorded yet.