• # question_answer All the points in the set $S=\left\{ \frac{\alpha +i}{\alpha -i}:\alpha \in R \right\}\left( i=\sqrt{-1} \right)lie$on             [JEE Main 9-4-2019 Morning] A) circle whose radius is 1.B) straight line whose slope is 1.C) straight line whose slope is -1D) circle whose radius is $\sqrt{2}$.

Let$\frac{\alpha +i}{\alpha -i}=z$$\Rightarrow$$\frac{\left| \alpha +i \right|}{\left| \alpha -i \right|}=\left| z \right|$$\Rightarrow$$1=\left| z \right|$ $\Rightarrow$circle of radius 1