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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: Equation complexe
Date: Wed, 26 Feb 2025 19:34:11 +0100
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Am 26.02.2025 um 19:23 schrieb Python:

> We can explain why i^2 = -1 from this very precise and clear definition:
> 
> i is the equivalence class of the polynomial X in the quotient ring 
> [actually a field] R[X]/(X^1+1).
> 
>  From that you can deduce that i^2 = -1.

Same with C := {(x, y) : x,y e IR}, i := (0, 1) and properly defined 
addition and multiplication on C.

Then we can PROVE that î * i = (-1, 0) aka -1.

No big deal.