Re: New way of dealing with complex numbers

Richard Hachel <r.hachel@tiscali.fr> wrote:

Le 07/03/2025 à 12:50, Alan Mackenzie a écrit :

Richard Hachel <r.hachel@tiscali.fr> wrote:

Does my new way of dealing with complex numbers bring an advantage or is
it stupid?

It's stupid.  Your "complex numbers" are not complex numbers.  They're
something else altogether.  The term "complex number" has a meaning in
mathematics, science, engineering, etc., and you are being deliberately
ignorant of that meaning.

The goal is to find something more coherent (it already is), but above
all more useful.

You have failed at that goal.

I recall the idea: the imaginary number i is a unit such that it is
invariant whatever its power. For all x, we have i^x=-1.

That is just ignorance.  It's not even clear what you mean by the above.
Your ^ operator clearly has nothing to do with multiplicative powers.

This was already the case with the real unit n=1. For all x, 1^x=1.

And for all x apart from 0, x^0 = 1.  That includes i^0 = 1.

In this sense, not only is i²=-1 true, i^(1/2)=-1, but also i^4=-1,
i^5689=-1, i^(-3/2)=-1.

That isn't sense, it's nonsense.

Second, the real or complex roots of quadratic equations are:

They are well understood by virtually everybody but you, and have been
for many centuries.

[ .... ]

Exemple : Roots of f(x)=x²+4x+5 ---> x'=i, x"=-5i

Wrong.

Finally, the complex roots of a function are the real roots of the
function in point symmetry $(0,y), and vice versa.

That's meaningless gibberish.

R.H.

I see you didn't understand anything.

But it doesn't matter.

For those who are more open-minded and less stupid than Alan:

Is that all you've got?  Ad hominem attacks?

I'm not saying that mathematicians treat things like that. I'm saying that
I treat things like that.
Everyone does what they want.

You're implicitly suggesting that these things are arbitrary, and that
your worthless suggestions are the equal of many centuries' development
of complex numbers by mathematicians, scientists and engineers.  They're
not.

Nothing prevents mathematicians from proposing their ideas, nothing
prevents me from proposing mine (validated in logic by AI).
Mathematicians pose i²=-1 and sqrt(i)=-1.

Again, your ideas are objectively worthless.

NOTHING prevents me from proposing a different law, encompassing these two
truths to bring them to i^x=-1 whatever x.

If you're going to do that, then stop lying by calling your "system"
complex numbers.

I affirm this as a new and universal law.

You're not in a position to affirm any such "law".

I am told that I am wrong, and that i^4=1.

That is indeed the case, yes.

I answer that they are wrong, and that they misunderstood me.

I understand you very well.  You are a troll and a crank, devoid of basic
education in maths.

I tell them that if i^x=-1 (new global theory) then i^4=-1 and so on.

i^x=-1 leads immediately to contradictions, as you have been told several
times already, hence is nonsense.

They start telling me again: "No, no, i^4=1".

This kind of knee-jerk response is stupid.

No, it is the affirmation of sense over nonsense.

R.H.

--
Alan Mackenzie (Nuremberg, Germany).