Let z be a complex number satisfying |z - 2i| = 2. The minimum value of |z + 1| is:
Step-by-Step Solution
Key Concept: |z - 2i| = 2 is a circle centered at (0, 2) with radius 2. |z + 1| is distance from point (-1, 0).
Step 1: The circle is centered at (0, 2) with radius 2. Step 2: The point is (-1, 0). Distance from center = √(1^2 + 2^2) = √5. Step 3: Since √5 > 2, the point is outside the circle. Step 4: Minimum distance from an exterior point to the circle is distance - radius = √5 - 2.
Correct Answer: D