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

1. √5 + 1
2. 2
3. 2 + √2
4. √3 + 1

Correct answer: √5 + 1

Solution

The equation |z - 4/z| = 2 represents a geometric condition in the complex plane, where the distance from the point z to the point 4/z is constant. By analyzing the relationship and maximizing the modulus |z| under this constraint, we find that the greatest possible value occurs when z is positioned optimally, leading to the result of √5 + 1.

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