Re: complex numbers

Dear Don Giovanni:

"Don Giovanni" <laterel0328@xxxxxxxxx> wrote in message
news:1118580874.108666.125200@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>i never understod whay complex
> number only have two dimenssion,
> the real and imaginary part
>
> whay not more?

If you think about the definition of imaginary, it really is
something closely tied to the "parent axis". By definition, it
is something that times itself (essentially), maps exactly to the
reals. Not much room for multiple axes, unless you have
orthogonality rules that map one imaginary axis to another.

I have worked with mathematics that used i, j and k as orthogonal
unit vectors. I don't recall the entire set of transformations,
but:
i . i = -1
i x i = 0
i x j = k (might have the signs messed up here and...)
i x k = -j (...here)
j . j = -1
k . k = -1

What I thought was cool was that famous 18th century
mathematicians spent a bit of effort evaluating the geometries of
pool tables. And how interactions between bodies resulted in
orthogonal departures... as if the interactions of bodies
*generated* 3D plus time.

David A. Smith


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