Re: Equation complexe

Le 26/02/2025 à 19:12, Richard Hachel a écrit :

Le 26/02/2025 à 13:31, Moebius a écrit :

If x ∈ IR, then x^2 ∈ IR and x^2 >= 0, and hence x^4 = (x^2)^2 >= 0.
 So x can't be in IR.
 Now let x = ir with r ∈ IR (and i, the imaginary unit, ∈ C).
 Then x^2 = i^2 * r^2 = -1 * r^2 ∈ IR. Hence x^4 = (x^2)^2 >= 0.
 Hence neither x ∈ IR nor x = ir with r ∈ IR will work.
 Actually, any x ∈ {(+1+𝑖)⋅3/√2, (+1-𝑖)⋅3/√2, (-1+𝑖)⋅3/√2,  (-1-𝑖)⋅3/√2} will work.
 Hope this helps.

 Thank you.
But we are not talking about the same thing.
Mathematicians talk about an imaginary unit i.

The word "imaginary" is a historic relief. We kept it but there is nothing "imaginary" in the usual sense when it comes to i or C (no more than any other consistently defined object such as 41, 1, 0 or -1).
Did you know that at some point in history some mathematicians rejected negative numbers?
What do you know about modern (i.e. post XIXe century) definition of natural numbers, relative numbers, rationals, "real" numbers, complex numbers (and more) ? NOTHING. You are pretending to teach without any knowledge of anything. Also without honesty.

I also talk about an imaginary unit i.
Mathematicians propose to replace in a negative discriminant a multiplication by 1, by a multiplication by -i², since i²=-1 and 1=-i².
I propose strictly the same thing, and, obviously, I obtain the same results as them.

Obviously not.

That is not the problem.
Simply, mathematicians do not explain WHY their imaginary unit i is worth -1 when we square it. They make dictates. Useful dictates, interesting dictates, but dictates nonetheless.

You are lying again. This has been said to you in fr.sci.maths.
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.
If you cannot get it, read my course (or others) and/or ask instead of fantasizing on your ill-defined contradictory personal "ideas".

[snip more nonsense and lies]

You are an insufferable crank, "Dr. Hachel" (aka former M.D. Richard Lengrand).