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

Question

If $S=\{z \in C:|z-i|=|z+i|=|z-1|\}$, then, $n(S)$ is :

Accepted Answer

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

$$\mathrm{ABC}$$ is a triangle. Hence its circum-centre will be the only point whose distance from A, B, C will be same.

So $n(S)=1$

Solutions · 1