Complex analysis query regarding annulus We say that annulus is given by say  $1<│z│<2$. Is it possible to have an annulus inside an annulus? Like in a domain $0\leqslant|z|\leqslant5$ can we have an annular region like $1<│z│<2$ and $3<│z│<4$? Will it still be an annulus?

Yes it still is an annulus. As when you take the annulus $3<│z│<4$  from the given domain ,there is still the region of $0\leq|z|\leq3$ and $4\leq|z|\leq5$. From here you can again remove $1<│z│<2$.
