subsets of C

[Collin Li]

Mao, the reason why the algebra seems to tell you a lie is because you square both sides. You end up solving for plus and minus of the LHS and RHS, which is why sometimes the algebra is invalid. Whenever you square both sides, you should pay careful attention to the domain, and apply it to the end. I suspect that if you do the algebra while paying careful attention, you will end up with the empty set for the domain.

[Ahmad]

In other words,

contradiction.

[evaporade]

well done, no such subsets of C exist.