Re: y=f(x)=(x²)²+2x²+3

Le 06/02/2025 à 22:35, "Chris M. Thomasson" a écrit :

For some reason, "some" people seem to want to say complex numbers are not "real" because of the word "imaginary" used to define the y axis?

Complex roots must be placed on the x'Ox axis since that is the definition of roots. It is particularly stupid to want to place them anywhere other than on that axis.
We will say: yes, but we can't, there are no real roots.
As for the equation f(x)=x²+4x+5 or for the equation g(x)=(x²)²+2x²+3
We simply need to clearly define what a complex root is, and no one does it (it is still Dr. Hachel who must explain it).
Complex roots are the roots of the mirror curve.
Thus we have as roots for f(x)=-2+i and -2-i which correspond perfectly to -3 and -1 of the mirror curve, and that is where we must place the two roots on the Cartesian coordinate system.
For the curve g(x) the roots are -i and +i. Which corresponds to the roots of the mirror curve at the top which is g'(x)=-(x²)²-2x²+3 and whose roots are 1 and -1.
I don't understand all this crazy stuff that mathematicians say, and that artificial intelligence stupidly relays.
All this comes from a misunderstanding of what i is and what an imaginary number is. For example, I am told that (i²)=-1 and therefore that (i²)²=1. This is completely false. Here, the mathematician is multiplying imaginaries with the laws of real numbers.
This is particularly stupid. We must set (i²)²=-1 which will avoid huge mathematical blunders.
This seems surprising, but it is obvious when we have the keys to the concepts to use correctly.
R.H.