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If |(z - i)/(z + i)| = 1, then the locus of z is

1. x-axis
2. y-axis
3. x = 1
4. y = 1

Correct answer: x-axis

Solution

The condition |z - i| = |z + i| means z is equidistant from (0,1) and (0,-1); the perpendicular bisector is the real (x) axis.

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