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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: Division of two complex numbers
Date: Mon, 20 Jan 2025 22:33:15 +0100
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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):
>>
>>           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