achille
Posts:
575
Registered:
2/10/09
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Re: N-dimensional complex numbers (2) :)
Posted:
Jun 19, 2011 12:59 PM
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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 3-d 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 3-d numbers doesn't exist.
>
> I have split the number into two 2-d complex numbers,
> which have the normal algebra of 2-d complex numbers.
> A non-algebraic algorithm unites these two 2-d 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
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