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If (sqrt(3)-i)^n=2^n, n in I, the set of...

If `(sqrt(3)-i)^n=2^n, n in I`, the set of integers, then n is a multiple of

A

6

B

10

C

9

D

12

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`(sqrt(3)-i)^(n)=2^(n)`
`rArr ((sqrt(3)-i)/(2))^(n)=1`
`rArr i^(n)(-1/2-(isqrt(3))/(2))^(n)=1`
`rArr i^(n)omega^(2n)=1`
`rArr i^(n)=1` and `omega^(2n)=1`
`rArr` n is a multiple of 3 and 4 both.
`rArr` n is a multiple of 12.
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