Re: Hello!

Le 19/01/2025 à 20:02, sobriquet a écrit :

 The latest desmos links should have the correct equation. If not, could you please be specific and point out which equation in the list of expressions on the left side is incorrect?.
 One striking feature of conventional products is that the product of
complex numbers on the unit circle ends up on the unit circle and your
alternative way to define multiplication doesn't have that feature:

I gave yesterday the formula for the addition of complex numbers as I gave, a long time ago already, the correct formula for the general addition of relativistic speeds.
I put it here again as an example.
Addition formula:
(a+ib)+(a'-ib')=(a+a')+i(b+b')
Multiplication formula:
(a+ib)(a'+ib')=aa'+(ib')a+(ib)a'+(ib)(ib')
Here, during the simplification, we must be careful not to make a colossal blunder. It is the product (ib)(ib') that will produce this blunder,
because the mathematician will not take care that (ib)(ib') is NOT
|i²|bb BUT |i|²bb'.
Here Hachel (it's me) then poses:
(a+ib)(a'+ib')=aa'+i(ab'+a'b)+bb'
and no longer:
(a+ib)(a'+ib')=aa'+i(ab'+a'b)-bb' which is a false result in its real part aa'+bb'.
R.H.