The number of complex numbers z such that |z - 1| = |z + 1| = |z - i| equals

JEE Main 2010 Mathematics question

The number of complex numbers z such that equals

Answer: (1)

The point is equidistant from 1, −1 and i, i.e. it is the circumcentre of these three non-collinear points:

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Question ID VK-039262