achille
Posts:
575
Registered:
2/10/09


Re: Ndimensional complex numbers (2) :)
Posted:
Jun 19, 2011 12:59 PM


On Jun 19, 11:31 pm, Alen <al...@westserv.net.au> wrote: > On Jun 19, 11:06 pm, Pfss...@aol.com wrote: > > > On Sat, 18 Jun 2011 21:44:41 0700 (PDT), Alen <al...@westserv.net.au> > > wrote: > > > >This will be my final attempt at 3d and other complex > > >numbers, but I think it is more promising than the previous > > >attempt. > > > Good! First define addition and multiplication so that you have an > > algebaic field! > > An algebraic field for 3d numbers doesn't exist. > > I have split the number into two 2d complex numbers, > which have the normal algebra of 2d complex numbers. > A nonalgebraic algorithm unites these two 2d results > to produce a final result. > > Alen
If I understand your definition of multiplication correctly, I don't think it is associative. For example, I get:
((1+j)*(3+4i+6j))*(4+3i+j) = (3/5 4/5i + 11j)*(4+3i+j) = 6i+56j AND (1+j)*((3+4i+6j)*(4+3i+j)) = (1+j)*(19i+35j) = 16i + 54j

