Find the module of \(\displaystyle z \in A \) so that the argument of \(\displaystyle z \) has a minimum value.

The correct answer should be \(\displaystyle \sqrt{7} \)

Haven't encountered this type of exercises before. I guess the geometric representation of complex numbers will help.The problem is that I have no idea how to represent this geometrically.All I know that from the second condition I get a circle, but why?

Can you explain me this sketch?