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Question
Locate the points for which 3 < |z| < 4.
Solution
|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.
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