Re: New way of dealing with complex numbers

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.

--
Alan Mackenzie (Nuremberg, Germany).