Question

All the points in the set $S=\{\frac{\alpha +i}{\alpha -i}:\alpha \in R\}$ $(i=\sqrt{-1})$ lie on a?

• A. Circle whose radius is $1$
• B. Straight line whose slope is $1$
• C. Straight line whose slope is $-1$
• D. Circle whose radius is $\sqrt{2}$

Answer 1

The correct option is A Circle whose radius is $1$

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