We draw two circles |z+3-2i|=r, one with the shortest possible
radius r that puts the circle in the region R, and the other
with the longest possible radius which puts the circle in
the region R.  They will be tangent to the disk with is Region
R.  Then all we have to do is calculate those two radii.  If 
your book answers are correct those two radii should be 7 and 13.

So just find the distance between the centers of the two
circles, -3+2i and 5-3i, which will be 10, then subtract the
radius 3 to get the minimum 7 and add it to get the maximum 13.

If you have any questions, ask them in the thank-you note
form below.

Edwin