Re: Equation complexe

Op 26/02/2025 om 05:12 schreef sobriquet:

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.[..]

 You have to understand that if we consider this equivalent case of
g(x) = x^4 + 9/4 and we visualize the complex roots as follows:
 https://www.desmos.com/calculator/4mhohrcxlg
 We're superimposing a real slice of the graph in the Cartesian plane on top of Complex plane where we visualize the complex roots of the polynomial.
 

Here we can visualize the real slice of the graph in 3D to understand
the relationship between the graph of the function in the real numbers
versus the graph of the roots of the function in the complex numbers:
https://www.desmos.com/3d/0l8ota7qha