Question

State True(1) or False(0)

The points which satisfy $2\le |z+i|\le 3$ lie on the boundaries and inside a ring shaped region bounded by two concentric circles with center (0,1) and having radius 2,3.

Answer 1

$|z+i|=3$ describes a circle centered at $(0,1)$ with radius 3.
Now
$|z+i|\le 3$ includes all the points on the boundary and within the boundary of the circle.
Also
$|z+i|=2$ describes a circle centered at $(0,1)$ with radius 2.
Now
$2\le |z+i|$ includes all the points on the boundary and outside of the circle.
Hence
The set of points
$2\le |z+i|\le 3$ lies on the ring shaped region bounded by two concentric circles.