Re: New way of dealing with complex numbers

Am 07.03.2025 um 12:50 schrieb Alan Mackenzie:

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

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.

Then i = (I guess) = i^1 = -1, one might think.
But then i^2 = (I guess) = i*i = (-1)*(-1) = 1, one might think.
So we get a contradiction, since 1 =/= -1.

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.

So again a contradiction (since 1 =/= -1).
So a rather bad "idea" by Hachel.