1.

If `((1 +i)/(1 -i))^(x) =1`, then (A) x=2n+1 (B) x=4n (C) x=2n (D) x=4n+1, n` in`N.A. `x = 2n + 1`B. `x = 4n`C. `x = 2n`D. `x = 4n + 1`

Answer» Correct Answer - B
Given that, `((1 +i)/(1 -i))^(x) =1`
`rArr [((1 + i)(1+ i))/((1 -i)(1 +i))]^(x) = 1 rArr [(1 + 2i+ i^(2))/(1-i^(2))]^x = 1 `
`[(2i)/(1+1)]^(x) = 1 rArr [(2i)/(2)]^(x) = 1`
`rArr i^(x) = 1 rArr i^(x) = i^(4n) " " [:. i^(4n) = 1, n in N]`
`rArr x = 4n`


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