Yes, it is interesting and yes I was agreeing with you after you explained what you meant. I thought I didn't need to explicitly say I agreed with you, since it was clear. I have no idea where I misinterpreted you and where I did not pay attention.
Anyway, complex numbers are not "theoretically impossible", unless you specify what it means. The theory of complex numbers is consistent if only the standard set theory is consistent, which is widely believed to be true. This means that there exists a model of complex numbers, and, actually, the main problem in constructing such a model is with constructing real numbers first. As I said though, I'm not really sure what "theoretically impossible" means to you. Do you mean some kind of philosophical theory? I'm completely unprepared to defend then.