Question

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

Answer 1

|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.