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From: Tom Bola <leah.line@gmail.com>
Newsgroups: sci.math
Subject: Re: Division of two complex numbers
Date: Tue, 21 Jan 2025 00:08:22 +0100
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Am 20.01.2025 23:26:19 Moebius schrieb:
> Am 20.01.2025 um 23:21 schrieb Tom Bola:
> 
>>> The binomial formula is (a + b)^2 = a^2 + 2ab + b^2 it is not about
>>> (0, 1)^2 or (a, b)^2.
>> 
>> Sure, but remember the definition of a complex number: Z = a+bi, i^2 = -1.
>> 
>> See?
> 
> See WHAT?!
> 
> Was wir hier brauchen, ist die Definition der MULTIPLIKATION (*) auf C = 
> {(x, y) : x,y e IR}.
> 
> DARAUS folgt dann
> 
>        i * i = (0, 1) * (0, 1) = ... = (-1, 0)
> 
> See?

Ja! This is fully straight plus absolutely correct. 

I was just looking for some idea. Aside from that please have a look here: 

(english readers just look for "binomisch")

https://www.math.kit.edu/iana2/~mandel/seite/schnupperkurs/media/komplex.pdf 

See?