Re: Equation complexe

Le 25/02/2025 à 23:05, guido wugi a écrit :

Op 25/02/2025 om 21:07 schreef Richard Hachel:

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.

 Contradictory, thus impossible.
If i^2=-1 then (i^2)^2 = (-1)^2 = 1 =  i^4

Absolutely not...
Pfffff...
You are using real powers on imaginary numbers.
You don't seem to understand what I'm saying.
I am stating the precise, formal, and definitive definition that in this imaginary system, the fundamental law is i^x=-1.
A fundamental law is not negotiable.
Now, you start to negotiate, like Python, and to tell me while crying: i^4=1.
This is not serious behavior.
R.H.