sketch the set of points determined by |z+i| is less than or equal to 3?

Answer 1

If z = -i then |z+i| = 0 which is in the set of interest.

Now think about it.

The set is a disk centered at -i of radius 3. Look at two extrema:

If z=2i then |z+i| = |3i| = 3 which is on the boundary
If z=-4i then |z+i |=|-3i| = 3 which is on the bounary.

Answer 2

If you put z= x+yi you get I x+(y+1)i<=3

x^2 +(y+1)^2 <=9 which represents a circunference and its interior
center (0,-1) radius 3