For the set determine if is closed.

I know what I need to show, namely that the set is open because every limit point of the set is not in the set. I'm having trouble articulating this in the language of math. Here's my ideas:

Consider the complex with .

It is clear that for every neighborhood such that , but since is open.

The thing that I worry about is the "it is clear." How do I show in general that every neighborhood at p where |p|=1 contains points in E?