Let $p(z,w)=\alpha_0(z)+ \alpha_1(z)w+\cdots+\alpha_k(z)w^k$ ,where $k \le 1$ and $p(z,w)=\alpha_0(z)+ \alpha_1(z)w+\cdots+\alpha_k(z)w^k_0,\cdots, p(z,w)=\alpha_0(z)+ \alpha_1(z)w+\cdots+\alpha_k(z)w^k_k$ are non-constant polynomials in the complex variable $z$. Then:
$(z,w) \in C\times C:p(z,w)=0$ is:
- Bounded with empty interior.
- Unbounded with empty interior.
- bounded with nonempty interior .
- unbounded with nonempty interior.
How can I be able to solve this problem ? I have no idea at all.