Find complex number(s) $z$ for which $|z|$ has maximum and minimum value if $|z-2+2i|=1$
My try: I know that $|z-2+2i|=1$ is a circle centered at $(2,-2)$ and having unit radius. Also $|z|$ is the modulus of moving point on this circle and I have to maximize and then minimize $|z|$
By using $$|z+w|>=||z|-|w||$$ I managed to get maximum and minimum values of $|z|$ and they turned out to be $2√2+1$ and $2√2-1$ respectively. But I am not able to get $z$.
I hope somebody will help me and nobody would down vote me If i sound so ignorant because I am at verge of loosing the right of asking a question in this site.