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From: sobriquet <dohduhdah@yahoo.com>
Newsgroups: sci.math
Subject: Re: What if Carl Friedrich Gauss was wrong?
Date: Sat, 1 Mar 2025 02:46:31 +0100
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Op 01/03/2025 om 02:12 schreef Richard Hachel:
> What if Descartes and Gauss were completely wrong?
> No, not about everything, obviously, but about some important details? 
> What if there were two blunders hidden, correcting each other, according 
> to the theory of compensated errors?
> First blunder: after having understood that the real roots were revealed 
> by x=[-b(+/-)sqrt(b²-4ac)]/2a, which is true and which is easily 
> demonstrated, generalizing the same discriminant too quickly, without 
> paying attention to the signs (complexes being complex to handle) and 
> setting i²=-1 (which is true) then
> x=[-b(+/-)i.sqrt(b²-4ac)]/2a instead of x=[-b(+/-)i.sqrt(b²+4ac)]/2a.
> The complex root is no longer the same. There would therefore be a first 
> error due to a misunderstood sign.
> The error is then compensated by another sign error, during the proof by 
> check via the reverse path. Thus, for me, the correct roots of 
> f(x)=x²-2x+8 are x'=4i, and x"=2i which can easily be placed on the 
> usual x'Ox axis of Cartesian coordinate systems, roots found elsewhere 
> by using x=[-b(+/-)i.sqrt(b²+4ac)]/2a without being trapped by a sign 
> error (we are no longer in real roots, but in complex roots, where x=-i 
> on the x'Ox axis and vice versa).
> 
> R.H.

If you think you have a superior theory of complex numbers, you're 
better off making an engaging video on the subject and then you can 
actually have some impact with potentially millions of views:

https://www.youtube.com/watch?v=5PcpBw5Hbwo