Re: Equation complexe

On 2/27/2025 3:53 PM, Chris M. Thomasson wrote:

On 2/27/2025 7:42 AM, Richard Hachel wrote:

Le 27/02/2025 à 08:47, joes a écrit :

Am Wed, 26 Feb 2025 20:22:01 +0000 schrieb Richard Hachel:

Le 26/02/2025 à 21:10, efji a écrit :
>

If you assume i^2 = i*i = -1, then i^4=1.

Absolutely not.

-1*-1 is not 1?

>
Claro que si.
Pero, i*i=i²=-1 ; (i²)²=-1
It seems that the imaginary unit i is a special unit such that i^x=-1 whatever x.
>
Mathematicians are right when they say that i=-1, that i^(-1/2)=-1, that i²=-1.
But if we understand Dr. Hachel's idea, we see that these three true statements are not enough.
Hachel imposes that i is an imaginary unit such that i^x=-1 whatever x.
This confuses the mathematician, who is used to working with real numbers, and who sets a²*a²=a^4 with systematically a>0.
But here we are not working with real numbers, but with the imaginary i.
It is not the same thing: we must systematically set i^x=-1 for all x.

 It kind of seems like you deny that the y axis even exists?

A fun aspect. I think there is a way to describe 2-ary complex numbers on the real line using some special blocks, so to speak...