Re: Equation complexe

Le 26/02/2025 à 19:34, Moebius a écrit :

Am 26.02.2025 um 19:23 schrieb Python:
 

We can explain why i^2 = -1 from this very precise and clear definition:
 i is the equivalence class of the polynomial X in the quotient ring [actually a field] R[X]/(X^1+1).
  From that you can deduce that i^2 = -1.

 Same with C := {(x, y) : x,y e IR}, i := (0, 1) and properly defined addition and multiplication on C.
 Then we can PROVE that î * i = (-1, 0) aka -1.
 No big deal.

Sure. There are numerous (equivalent) definition. 2x2 matrices etc.
Everything is a big deal for an hypocrite crank like Hachel/Lengrand.