i²=-1

To solve quadratic equations without real roots of the type f(x)=x²+4x+5, mathematicians invented complex roots.
The idea, obviously, was not bad.
We then assumed an imaginary number, which we named i, such that i²=-1, and this number would allow, not only to positiveize the discriminant, but also to make the square root disappear.
All profit.
Except that it is not enough.
Why is it not enough? Because we do not explain what this i is, nor where it really comes from.
We are content with a postulate, without seeing the horrible consequences for all mathematical logic.
We say i²=-1, without understanding, without thinking, believing that it is a very simple and harmless thing to handle explosives, and we handle TNT so well that we affirm the following mathematical monstrosity: "If i²=-1 then i²*i²=1.
This is one of the greatest mathematical crimes of the entire human species, because ignorance of what i is has already led us to this.
We will then progress into the worst.
We can only progress into the worst.
When we are sick, we generally ask the doctor's opinion.
But when we are scientifically sick, and we believe such nonsense, we do not ask the doctor's opinion, and it is the doctor who is judged crazy.
But the doctor, he still wants to explain himself, and to say WHY i²*i²=-1 and not 1.
Basically, it was necessary to introduce the following notion, well more efficient than a simple i²=-1 which explains nothing, and explaining nothing at all of its
mathematical being, becomes very dangerous to use unconsciously.
Basically, we must state: the number i is a complex which has the particularity of being such that, for all x, i^x=-1.
Similarly for all x, 1^x=1, i^x=-1.
That is the basis, and that is what explains that i²=-1.
But now that we have understood who i is, the entire current mathematical basis collapses, and, for example, i^4=-1 and NOT i^=1.
Similarly for "-1", we must respect the mathematical logic of the imaginaries and not use the operations of the reals.
I give here, the correspondence table of the imaginaries, according to their power and their sign. I hope you receive it well.
<http://nemoweb.net/jntp?Mhl_dvPLsa5T3I0u7LlBV0DezeM@jntp/Data.Media:1>
R.H.