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Question:

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

Circle whose radius is 1

Straight line whose slope is -1

Circle whose radius is √2

Straight line whose slope is 1

Solution:

The correct option is A Circle whose radius is 1
Let α + iα - i = z ⇒ ||α + iα - i|| = |z| ⇒ 1 = |z| ⇒ circle of radius 1.