# Math Help - Field Extension

1. ## Field Extension

How can I show that there is no finite field extension of $\mathbb C.$

2. I thought to prove it by contradiction. but then I am having problem to prove it.

3. Originally Posted by peteryellow
How can I show that there is no finite field extension of $\mathbb C.$
Since $\mathbb{C}$ is algebraically closed it has no proper algebraic extension let alone a finite extension.