Re: Division of two complex numbers

Am 20.01.2025 um 21:07 schrieb Chris M. Thomasson:

On 1/20/2025 11:33 AM, Moebius wrote:

Complex numbers can be defined as (ordered) pairs of real numbers.
>
Then we may define (in this context):
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          i := (0, 1) .

 Indeed. 0+1i = (0, 1)
 In some of my vector code I allow for traditional 2-ary vector multiplication and complex multiplication.

Same in math. Even though we may use the same symbol, say "*", it denotes two different operations (in this case).

A complex number can be a  simple 2-ary vector.

Exactly.

[...] Multiplying two 2-ary vectors together is different than multiply two complex number together,

Right. It's the context that "decides" here; at least in math.

however they can  both be stored in the same vector representation.
 z = 2 + 8i = (2, 8)
 Where 2 = Re(z), and 8 = Im(z)

Right. In math we call such an object an ordered pair (or 2-tuple).
See: https://en.wikipedia.org/wiki/Ordered_pair
and: https://en.wikipedia.org/wiki/Tuple