Re: Equation complexe

Le 26/02/2025 à 20:16, Python a écrit :

Le 26/02/2025 à 20:10, Richard Hachel a écrit :

Your new "system" with i^2 = -1 and i^4 = -1 is not even consistent.

 It is the system i²*i²=i^4=1 that does not seem coherent to me.
Of course, in the real world, we have for example (x²)² positive.
But here, we have introduced an imaginary unit, such as i^x=-1.
This is a definition that will not simply apply to the roots of quadratic functions, but to ALL functions.
Including for example f(x)=sqrt(x)+2 or g(x)=(x²)²+x²+2 which are other types of functions than a simple quadratic.
I can easily get the complex roots out of it (there are no real roots).
The roots given by mathematicians are not correct, because they are based on an Argand frame, with a separation of a and ib into two orthogonal entities, which does not exist in Cartesian frames where complex roots are on x'Ox like the others, and are the object of simple additions such as x'=5+3i=2, or x"=8-2i=10 (i=-1).
R.H.