All the points in the set S = \(α + i)/(α - i) : α ∈ R \ (i = √(-1)) lie on a

straight line whose slope is -1.

straight line whose slope is 1.

All the points in the set S = \(α + i)/(α - i) : α ∈ R \ (i… — JEE Main 2019 Mathematics PYQ

JEE Main 2019 · 9 April · Shift I

All the points in the set

S = \left\{\dfrac{\alpha + i}{\alpha - i} : \alpha \in \mathbb{R}\right\}

(i = \sqrt{-1})

lie on a

A.
circle whose radius is $\sqrt{2}$ .
B.
straight line whose slope is $-1$ .
C.
circle whose radius is $1$ .
D.
straight line whose slope is $1$ .

Show answer and solution

Correct option: C

Solution

Let z = (α + i)/(α - i). Compute |z|: |z| = |α + i|/|α - i| = √(α² + 1)/√(α² + 1) = 1. Since |z| = 1 for all real α, every point lies on the unit circle, which has radius 1.

[JEE Main 2019 · 9 April · Shift I]

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JEE Main 2019 Mathematics question on Complex Numbers and Quadratic Equations