>>Well, I always thought there's an isomorphism between the complex set and the real x/y plane... Which obviously means that any complex number has its "place" in this plane.
>>
>I checked this out in my math library last night (I'm a bit rusty on some theory)...the only isomorphism I find between C & R is for the trivial case in C where we have the ordered pair (a,0) in a+bi.

If we talk about a plane (not aircraft:)), it has 2 dimensions. The x/y plane is RxR, not R. So it's isomorphic with C. But I think the problem (between what you're saying and what I'm saying) here is a difference of notations and language, not of meaning.

>A general isomorphism cannot exist since R is an ordered field but C is not...

Why isn't C ordered?

>(I'm sure this info will be useful to all UT folks!) :~)

Well, I like to remember all this things I never used. :)

Vlad