The least positive integer n for which 1 + i 3 1

Given 1 + i 3 1 - i 3 n = 1 ⇒ - 2 ω 2 - 2 ω n = 1 ⇒ ω n = 1 Hence, the least positive integer value of n is 3 .

Question: Answered & Verified by Expert

The least positive integer

n

for which

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

MathematicsComplex NumberJEE MainJEE Main 2018 (16 Apr Online)

Options:

Solution:

1740 Upvotes Verified Answer

The correct answer is:

3

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

3

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