JEE Main20199 Apr 2019Morning ShiftMathematicsComplex NumberActual
All the points in the set S = α + i α - i , α ∈ R , i = - 1 lie on a
Options
- Astraight line whose slope is - 1
- Bcircle whose radius is 2
- Ccircle whose radius is 1
- Dstraight line whose slope is 1
Correct answer
C. circle whose radius is 1
Step-by-step solution
Given z = α + i α - i , since α ∈ R ⇒ z = α + i α - i = α + i α - i ⇒ z = α 2 + 1 2 α 2 + - 1 2 ⇒ z = 1 Hence, locus of z is a circle with radius 1 .