Re: New way of dealing with complex numbers

On 3/7/2025 4:04 AM, Richard Hachel 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.

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

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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.

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That isn't sense, it's nonsense.
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Second, the real or complex roots of quadratic equations are:

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They are well understood by virtually everybody but you, and have been
for many centuries.
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[ .... ]
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Exemple : Roots of f(x)=x²+4x+5 ---> x'=i, x"=-5i

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Wrong.
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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:
 I'm not saying that mathematicians treat things like that. I'm saying that I treat things like that.
Everyone does what they want.
 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.
 NOTHING prevents me from proposing a different law, encompassing these two truths to bring them to i^x=-1 whatever x.
 I affirm this as a new and universal law.
 I am told that I am wrong, and that i^4=1.
 I answer that they are wrong, and that they misunderstood me.
 I tell them that if i^x=-1 (new global theory) then i^4=-1 and so on.
 They start telling me again: "No, no, i^4=1".
 This kind of knee-jerk response is stupid.

Okay. Well. Let's start small. Use your new way to implement the Mandelbrot set and/or any Julia set. Plot the sucker! Then show us the resulting plot...