All the points in the set S= \(alpha+i)/(alpha-i):alphain R \ , i=sqrt(-1) lie on a

Complex Numbers: All the points in the set S= \(alpha+i)/(alpha-i):alphain R \ ,… | JEE Main 2019

JEE Main 2019 (Online) 9th April Morning ShiftQuestion 1

All the points in the set $S=\left\{\frac{\alpha+i}{\alpha-i}:\alpha\in R\right\}$, $i=\sqrt{-1}$ lie on a

Complex Numbers

straight line whose slope is $-1$circle whose radius is $\sqrt2$circle whose radius is $1$✓ Correct answerstraight line whose slope is $1$

Solution

$\left|\frac{\alpha+i}{\alpha-i}\right|=\frac{\sqrt{\alpha^2+1}}{\sqrt{\alpha^2+1}}=1$, so all points lie on the circle of radius $1$.