If S = z ∈ C: | z - i | = | z + i | = | z - 1 | , then, n ( S ) is:

Given: $| z - i | = | z + i | = | z - 1 |$

The given equation represents that $z$ is a point such that it is equidistant from \left(0, 1\right), \left(0, - 1\right) \text{and } \left(1, 0\right)

We know that in a triangle only circumcentre is the point which is equidistant from the three vertices.$</p><p><img src="https://cdn-question-pool.Quantrex.app/pyq/jee_main/2b2ec73a-8e12-4c5b-9db0-3995a5c016d9.png" style="width: 323px; height: 194px;"/><br/>$ABC$is a triangle. Hence its circum-centre will be the only point whose distance from A, B, C$ will be same.
So $n ( S ) = 1$