Re: Division of two complex numbers

Le 20/01/2025 à 19:10, Python a écrit :

Le 20/01/2025 à 18:58, Richard Hachel  a écrit :

Mathematicians give:
 z1/z2=[(aa'+bb')/(a'²+b'²)]+i[(ba'-ab')/(a'²+b'²)]
 It was necessary to write:
z1/z2=[(aa'-bb')/(a'²-b'²)]+i[(ba'-ab')/(a'²-b'²)]

I've explained how i is defined in a positive way in modern algebra. i^2 = -1 is not a definition. It is a *property* that can be deduced from a definition of i.

 That is what I saw.
 Is not a definition.  It doesn't explain why.
We have the same thing with Einstein and relativity.
Einstein, he's a nice guy, a tender guy, he says "The speed of light is constant by change of frame of reference".
But he doesn't explain why.
He gives a quality, but without specifying the cause.
Reread my chapters on the notions of simultaneity, on the notion of anosochrony, of synchronization of watches, you will see, if you make the effort, why the invariance of c is logical,
and why it is like that.
For i, it's the same.
It is clear that i²=-1, but we don't say WHY. It is clear however that if i is both 1 and -1 (which gives two possible solutions) we can consider its square as the product of itself by its opposite, and vice versa.
R.H.