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JEE Main 201816 AprilOnline
Exam
JEE Main
Year
2018
Date
16 April
Mode
Online
Subject
Mathematics
Chapter
Complex Number

JEE Main 2018 · 16 April · Online · Mathematics · Complex Number

The least positive integer n for which ( 1 + i 3 1 - i 3 ) ^ n = 1...

The least positive integer nn for which (1+i31−i3)n=1{\left(\dfrac{1 + i\sqrt{3}}{1 - i\sqrt{3}}\right)}^{n} = 1 is

Options

  1. A22
  2. B55
  3. C66
  4. D33

Correct answer

D. 33

Step-by-step solution

Given (1+i31−i3)n=1{\left(\dfrac{1 + i\sqrt{3}}{1 - i\sqrt{3}}\right)}^{n} = 1

→(−2ω2−2ω)n=1{\left(\dfrac{- 2{\omega}^{2}}{- 2\omega}\right)}^{n} = 1

⇒⇒ωn=1{\omega}^{n} = 1

Hence, the least positive integer value of nn is 33.
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