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If |z - 4/z| = 2 for a complex number z, what is the greatest possible value of |z|?

1. 1 + sqrt(2)
2. 2 + sqrt(2)
3. sqrt(3) + 1
4. sqrt(5) + 1

Correct answer: sqrt(5) + 1

Solution

Applying |z| - |4/z| <= |z - 4/z| gives r - 4/r <= 2, so r² - 2r - 4 <= 0, whose positive bound is 1 + sqrt(5).

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