All the possible points in the set S={α+iα−i:α∈R,i=√−1} lies on
A
a circle whose radius is √2 units.
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B
a circle whose radius is 1 unit.
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C
a straight line whose slope is 1.
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D
a straight line whose slope is −1.
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Solution
The correct option is B a circle whose radius is 1 unit. Let α+iα−i=Z Taking modulus on both sides ∣∣∣α+iα−i∣∣∣=|Z| As α is real, ∴√α2+12√α2+(−1)2=|Z|⇒|Z|=1
Hence, the points in S lies on a circle with radius 1 unit.