All the points in the set S = α + i α - i ,   α ∈ R ,   i = - 1 lie on a

All the points in the set S=α+iα-i, α∈R, i=-1 lie on a
  1. straight line whose slope is -1
  2. circle whose radius is 2
  3. circle whose radius is 1
  4. straight line whose slope is 1

Solution

Given z=α+iα-i , since α∈R

⇒z=α+iα-i=α+iα-i

⇒z=α2+12α2+-12

⇒z=1

Hence, locus of z is a circle with radius 1.

Asked in: JEE Main 2019 (09 Apr Shift 1)

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