Z comes as a way of solving x + 1 = 0
Q comes as a way of solving 2·x = 3
Z comes as a way of solving x*x = 2
C comes as a way of solving x*x + 1 = 0

Seems like each superset of numbers just comes as a way of solving an unsolvable equation that does not make sense otherwise. Does this mean you could just make yet a new set to solve other equations that are still unsolvable in C such as

z = z + 1

or

z = 1/0