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A complex number z is said to be unimodular if |z| = 1. Suppose z 1 and z 2 are complex numbers such that 2 1 2 1 z z 2 z 2 z − − is unimodular and z 2 is not unimodular. Then the point z 1 lies on a :

1. straight line parallel to x-axis
2. straight line parallel to y-axis
3. circle of radius 2
4. circle of radius 2

Correct answer: circle of radius 2

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