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Subject: Re: Equation complexe
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Date: Tue, 25 Feb 25 20:07:02 +0000
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From: Richard Hachel <r.hachel@tiscali.fr>
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Le 25/02/2025 à 18:21, Jim Burns a écrit :
> On 2/25/2025 9:23 AM, Richard Hachel wrote:
> 
>> x^4=-81
>>
>> What is x?
> 
> x ∈ {(+1+𝑖)⋅3/√2, (+1-𝑖)⋅3/√2, (-1+𝑖)⋅3/√2, 
> (-1-𝑖)⋅3/√2}

 Oui, c'est ce que dis aussi l'Intelligence artificielle, mais sans trop 
expliquer pourquoi. 

 Personally, I propose only one root, but it is not in conformity with 
what is said about "complex numbers".
I remind you that I do not admit the definition i²=-1, which, in itself, 
is not false, but so narrow that I do not understand its semantic 
interest.
For me, the definition must be extended to all powers of x such that 
i^x=-1.
In short, it is necessary to go through a constancy of i^x=-1, like 1^x=1.
This defined, we easily have x^4=-81 if x=3i.
The other four roots being incorrect (in the proposed system).

R.H.