Solution: Let $p(z)$ be a polynomial in $\mathbb{C} $. Let $z_0\in \mathbb{C} $. We need to show that there exist $w\in \mathbb{C} $ such that $p(w) = z_0$. Consider the polynomial \[ q(z) = p(z)-z_0. \] The polynomial $q(z)$ is non-constant. Using fundamental theorem of algebra, there must exist a root of $q$. So we have \[ q(w) = 0 \implies p(w)-z_0 = 0 \implies p(w) = z_0. \]