The question:

Is the region $\displaystyle |z - 1 + i| \ge 2$:

a) Open?

b) Connected?

I always have trouble with these questions, since I'm not entirely sure what 'open' and 'connected' sets entail. My solution is a) no, b) no.

My reasoning is that it's not open because the set is a closed circle in the complex plane, with the set lying outside this circle. My reasoning for it not being connected is simply because there's a hole in the set (I'm sure my reasoning here is insufficient).

No solutions were provided for this question.

Any assistance would be great!