IMABS

What it does

IMABS(inumber)

IMABS(inumber) returns the modulus of a complex number a+bi. Unlike functions that return complex text, this function returns a real worksheet number.

Try it

=IMABS("8+15i") returns 17, since 8^2+15^2=289 and its square root is seventeen. =IMABS("-4i") returns 4: changing direction does not change distance from zero.

Quirks

The result is numeric and nonnegative. Real-only and pure-imaginary inputs are valid; a negative coefficient does not make a negative modulus. The current parser rejects malformed complex text with #NUM! and logical values with #VALUE!.

Squaring each component naively can overflow even when the modulus is representable. The current implementation uses a runtime hypotenuse primitive. This differs from IMSQRT's separately observed sum-of-squares graph.

How to implement

Parse the input as the pair (a,b). A numeric scalar becomes (a,0); complex text may use lowercase i or j. Return the runtime hypot(a,b) under the worksheet number-publication policy.

For a mathematical scaled implementation, take m=max(abs(a),abs(b)) and t=min(abs(a),abs(b))/m. Return zero if m=0; otherwise compute m*sqrt(1+t*t). This bounds the squared ratio by one. It avoids intermediate square overflow, although its rounding is not a substitute for every runtime hypot result. For 8+15i, the scaled expression is 15*sqrt(1+(8/15)^2), about seventeen. The lexical parser and numerical primitive are separate parts of the implementation.

Rust code

31 imabs "IMABS" (1, 1) [V "inumber"] |s, a, sv| { complex_number(s, a, |z| Ok(z.abs())) }

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

COMPLEX constructs text from coordinates. IMARGUMENT returns the phase angle.

Named variants

No named variants are recorded yet.