I'm just making sure I got this. So, the reason a number can have n nth roots when using complex numbers is because of the way that i is defined? So, if one defined some other different k, would it be possible to find say n+1 nth roots? I guess my question is: does the fact that the polynomial x^n  c =0 has n roots, something that holds true independent of the way complex numbers are defined?
Thanks!
