Complex Numbers
Complex Plane / Geometry
Grade Class 11

Question:

<p>On the complex plane, the locus of a point \( z \) satisfying \( 2 \leq |z - 3| &lt; 3 \) denotes:</p>
Region between concentric circles r=2 and r=3 at (3,0), including both boundaries
Region between concentric circles r=2 and r=3 at (3,0), excluding inner and including outer
Region between concentric circles r=2 and r=3 at (3,0), including inner boundary and excluding outer
Region between concentric circles r=2 and r=3 at (3,0), excluding both boundaries

Step-by-Step Solution

Key Concept: 2 \leq |z-3| means z is on or outside circle of radius 2; |z-3| < 3 means strictly inside circle of radius 3. So inner boundary included, outer excluded.
<p>\( 2 \leq |z-3| &lt; 3 \) means \( z \) is at distance \( \geq 2 \) from \( (3,0) \) (inner circle included) and distance \( &lt; 3 \) from \( (3,0) \) (outer circle excluded). Annular region with inner boundary included.</p>
Correct Answer: C

Master Complex Numbers with Mathbee

Practice this topic under real exam conditions with strict timers, or ask our AI Mentor to explain the concepts step-by-step.

Start Practicing for Free