>>33
x, y are generally variables (ie not always the same value)
i is
always the same constant (ie always the same value) (up to isomorphism with -i)
i is an imaginary
number
If you're thinking about decimal expansions, then phail, since that can only represent finite real numbers.
>>32
I've generally visualized things according to their algebraic properties (ie pushing symbols around), so I can't help you with that.
Even 4 dimensions is incredibly difficult to visualize; I'm not sure how you manage to visualize negative dimensions. Do describe.
My example was not intended to demonstrate the properties of exponentiation, but rather to demonstrate that even in a relatively simple case, intuition falls apart. If you can find a less abstract way to visualize the sqrt(3)th power of a positive real number, I'd love to hear it.