JEE PYQ: Complex Numbers Question 29
Question 29 - 2019 (09 Apr Shift 1)
All the points in the set $S = \left{\frac{\alpha+i}{\alpha-i} : \alpha \in \mathbb{R}\right}$ $(i = \sqrt{-1})$ lie on a:
(1) straight line whose slope is $1$
(2) circle whose radius is $1$
(3) circle whose radius is $\sqrt{2}$
(4) straight line whose slope is $-1$
Show Answer
Answer: (2)
Solution
$w = \frac{\alpha+i}{\alpha-i}$. $|w| = \frac{|\alpha+i|}{|\alpha-i|} = \frac{\sqrt{\alpha^2+1}}{\sqrt{\alpha^2+1}} = 1$. So $|w| = 1$, a circle of radius 1.
BETA
