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

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 .

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MathematicsComplex NumberGeneral(Modulus,Argument,Conjugate)Medium2 minPYQ_2018

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The least positive integer $n$ for which ${(\frac{1 + i \sqrt{3}}{1 - i \sqrt{3}})}^{n} = 1$ is

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Answer:

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 $3$ .

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:General(Modulus,Argument,Conjugate)

⏱ 2mℹ️ Source: PYQ_2018

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