The least positive integeral value of n for which `(sqrt(3)+i)^(n)=(sqrt(3)-i)^(n)`, is

Options

A. 3
B. 4
C. 6
D. none of these

Answer

C

Explanation

We have,
`rArr ((sqrt(3)+i)/(sqrt(3)-i))^(n)=1`
`rArr ((-1+isqrt(3))/(1+isqrt(3)))^(n)=1`
`rArr ((2omega)/(-2omega^(2))^(n)) =1 [therefore -1/2+isqrt(3)/2=omega "and" -1/2-isqrt(3)/2=omega^(2)]`
`rArr (-1)^(n)omega^(2n)=1`
`rArr` n is even multiple of 3
`rArr n=6`