Re: Equation complexe

On Wed, 26 Feb 25 00:11:36 +0000, Richard Hachel <r.hachel@tiscali.fr>
wrote:

<snip>

I think that for the moment, we are making things terribly complicated.

By we of course you mean your refusal to accept the standard meaning
of a complex number.

If I ask you the cube root of 27?
Are you going to make a computer program?
Why make a computer program if I ask you the fourth root of -81?
>
The answer is simple and obvious. x=3i.

And incorrect.  In standard mathematics, (3i)^4 does not equal -81

All these misunderstandings come from the fact that no clear and
universally usable definition of the imaginary number i has ever been
given.

Strange that none of us seem to have a problem with the standard
definition that has been around for centuries.

Against all expectations, in analytical mathematics, i is an imaginary
unit such that, for all x, i^x=-1.

Only in your imagination.

We see that saying that i²=-1 is completely legal.
>
Or that sqrt(i)=i^(1/2)=-1.

Your sqrt function is also non-standard.  In standard math, if
y = sqrt(x) then y^2 = (sqrt(x))^2 = x.  In your case, saying
sqrt(i) = -1 yields i = (sqrt(i))^2 = (-1)^2 = 1 which, of course, you
refuse to accept.

But we also see that (i²)² is not equal to 1, and that those who believe
it are corrupting themselves.

Considering that the standard definition works in physics,
electronics, and other sciences, they must be corrupt also.  It's a
wonder that your computer works and you can access the internet
through all this corruption.

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