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

Step-by-step solution

Given: | z - i | = | z + i | = | z - 1 | The given equation represents that z is a point such that it is equidistant from 0 , 1 , 0 , - 1 & 1 , 0 We know that in a triangle only circumcentre is the point which is equidistant from the three vertices. A B C 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