The least positive integer n for which 1 + i 3 1 - i 3 n = 1 is

The least positive integer

n

for which

{(\frac{1 + i \sqrt{3}}{1 - i \sqrt{3}})}^{n} = 1

is

$2$
$5$
$6$
$3$

Solution

Given

{(\frac{1 + i \sqrt{3}}{1 - i \sqrt{3}})}^{n} = 1

⇒

{(\frac{- 2 ω^{2}}{- 2 ω})}^{n} = 1

\Rightarrow

ω^{n} = 1

Hence, the least positive integer value of

n

is

3

.

Asked in: JEE Main 2018 (16 Apr Online)

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