IMDIV

What it does

IMDIV(inumber1, inumber2)

IMDIV(inumber1, inumber2) divides a complex numerator by a complex denominator and returns complex text.

Try it

=IMDIV("4+2i","1+i") returns "3-i": multiplying 3-i by 1+i recovers 4+2i.

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 zero complex denominator gives #NUM! in the current implementation. Large components make the choice of division formula observable.

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.

Use the scaled division implemented in the product. For numerator (a,b) and denominator (c,d), if abs(c)>=abs(d), set r=d/c, v=c+d*r, and return ((a+b*r)/v,(b-a*r)/v). Otherwise set r=c/d, v=d+c*r, and return ((a*r+b)/v,(b*r-a)/v). This avoids directly forming c*c+d*d. In the example r=1, v=2, giving (6/2,-2/2)=(3,-1). The code flushes subnormal output components before formatting. The retained witnesses distinguish this graph from the squared-denominator formula.

Rust code

51 imdiv "IMDIV" (2, 2) [V "inumber1", V "inumber2"] |s, a, sv| {
    let x = complex_of(s, 0, &a[0])?;
    let y = complex_of(s, 1, &a[1])?;
    complex_text(x.div(y), &[x, y])
}

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

IMPRODUCT multiplies; IMCONJUGATE supplies the conjugate often used in a mathematical derivation of division.

Named variants

No named variants are recorded yet.