Sujet : Re: New equation
De : dohduhdah (at) *nospam* yahoo.com (sobriquet)
Groupes : sci.mathDate : 24. Feb 2025, 22:49:47
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Op 24/02/2025 om 22:11 schreef Richard Hachel:
Le 24/02/2025 à 21:23, Barry Schwarz a écrit :
On Mon, 24 Feb 25 18:52:17 +0000, Richard Hachel <r.hachel@tiscali.fr>
A quartic always has four roots.
Here, I would still put a small caveat.
The fact of saying that an equation of degree n has n roots is perhaps not entirely correct.
I ask myself the question.
If for example we write f(x)=x^3+3x-4, it is indeed an equation of degree 3.
But how many roots, and what are they?
I asked this question to mathematicians, and to artificial intelligence, and I was given three roots, but they are incorrect, because those who answer do not seem to understand the real concept of imaginary numbers.
There is in fact only one root.
A very strange root composed of a real root and a complex root. Both placed on the same point A(1,0) and A(-i,0).
R.H.
https://i.imgur.com/6bUA65Y.pngThe conventional definition of complex multiplication is carefully chosen to preserve geometric interpretations, algebraic properties, and consistency with real numbers. The alternative definition fails to meet these requirements, making it unsuitable for use in complex analysis and its applications.