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