|z| < 4⇒ x2 + y2 < 16 which is the interior of circle with centre at origin and radius 4 units, and |z| > 3⇒ x2 + y2 > 9 which is exterior of circle with centre at origin and radius 3 units. Hence 3 < |z| < 4 is the portion between two circles x2 + y2 = 9 and x2 + y2 = 16.
