>>37
Interesting, but I don't quite follow. Don't real numbers have dimensionality 1?
Your visualization with a black hole is quite interesting, but I should point out that "real" black holes require at least 5 dimensions for proper embedding.
>>39
The set of complex numbers do not form an ordered field. You cannot place bounds on i.
>>41
They are indeed often represented as a vector, with the imaginary axis orthogonal to the real axis.
If you really want, you can say xi + y1, where "1" is the real multiplicative identity.
>>49
RedCream's definition satisfy the requirements of a vector space. The whole thing may not form a field, but it is still a vector space. The "i*i = -1" example only demonstrates a bad way to define an inner product space. The set of continuous functions form a vector space, and the inner product of any 2 functions results in a real number, which is not in the original vector space. Similarly, the notion of multiplicative inverse is moot.