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If a complex number z satisfies |z| >= 3, then the smallest possible value of |z + 1/z| is:

1. 5/3
2. 8/3
3. 11/3
4. none of these

Correct answer: 8/3

Solution

Since |z + 1/z| >= |z| - 1/|z| = r - 1/r is increasing in r, the minimum over r >= 3 is 3 - 1/3 = 8/3.

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