TIFR Mathematics 2023 | Part B | Question: 12

Question

Answer whether the following statements are True or False.

Let $f \in \mathbb{C}\left[z_{1}, \ldots, z_{n}\right]$ be a nonzero polynomial $(n \geq 1),$ and let
\[
X=\left\{z \in \mathbb{C}^{n} \mid f(z)=0\right\} .
\]
Then $\mathbb{C}^{n} \backslash X$ is path connected.