Question

locate the point representing the complex numbers $z$ on the Argand diagram for which
$2\le |z+i|\le 3$

Answer 1

We know that point satisfying $|z+i|\ge 2$ lie
outside on the circle with center $-i$ i.e $(0,-1)$ and
radius $2$. Similarly, the points $z$ satisfying $|z+i|\le 3$ lie inside and on the circle with center-i
and radius $3$.
Hence the point which satisfy $2\le |z+i|\le 3$ lie on the boundaries and inside a ring shaped region bounded by
two concentric circle centred at $-i$ i.e,, $(0,-1)$ and having radius $r_1=2$ and $r_2=3$.