Let \(\displaystyle u=2+2i \) and \(\displaystyle A = \) { \(\displaystyle z \in \mathbb{C} : \vert z-1 \vert \leq \vert z-i \vert \) and \(\displaystyle \vert z-u \vert \leq 1 \) }
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?
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?