<p>The minimum value of \( |z| + |z-1| + |z-2| \) for \( z \in \mathbb{C} \) is:</p>
Step-by-Step Solution
Key Concept: On the real line, for collinear points 0, 1, 2 the minimum of |x| + |x-1| + |x-2| is at x = 1 giving 0+1+1 = 2. For complex z, the minimum cannot be less.
<p>By the triangle inequality, $ |z|+|z-2| \geq |2| = 2 $, with equality when $z$ lies between 0 and 2 on the real segment. Adding $|z-1| \geq 0$ and taking $z=1$: $1+0+1=2$. Minimum = 2.</p>
Correct Answer: C