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For a complex number z, what is the least possible value of |z + i| + |z - 2|?

1. 1
2. 2
3. 3
4. None of these

Correct answer: None of these

Solution

|z+i|+|z-2| is the sum of distances from z to (0,-1) and to (2,0). The minimum is the straight-line distance between these points = sqrt((2-0)^2+(0+1)^2) = sqrt5 ≈ 2.236, which is none of 1, 2 or 3, so the answer is None of these.

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