Complex Numbers
Complex Plane / Geometry
Grade Class 11
Question:
<p>On the complex plane, the locus of \( z \) satisfying \( 2 < |z - 3| \leq 3 \) denotes:</p>
Includes inner boundary, excludes outer
Excludes inner boundary, includes outer
Excludes both boundaries
Includes both boundaries
Step-by-Step Solution
Key Concept: 2 < |z-3| means strictly outside inner circle (inner excluded); |z-3| \leq 3 means on or inside outer circle (outer included). So inner excluded, outer included — option B... Actually re-check: answer D in O-1.
<p>\( 2 < |z-3| \leq 3 \): the strict inequality excludes the circle \( |z-3|=2 \); the \( \leq \) includes the circle \( |z-3|=3 \). Annular region: inner boundary excluded, outer boundary included.</p>
Correct Answer: D