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  • Help me solve this - Complex numbers and quadratic equations - JEE Main-10

The least positive integer n for which

\left ( \frac{1+i\sqrt3}{1-i\sqrt3} \right )^{n}= 1

 is

  • Option 1)

    2

  • Option 2)

    3

  • Option 3)

    5

  • Option 4)

    6

 

Answers (1)

best_answer

\omega = \frac{-1+i\sqrt3}{2}

and \omega^{2} = \frac{-1-i\sqrt3}{2}

so \left ( \frac{1+i\sqrt3}{1-i\sqrt3} \right )^{n}= \left ( \frac{w^{2}}{w} \right )^{n}=w^{n}=1

least value of n = 3


Option 1)

2

This is incorrect 

Option 2)

3

This is correct 

Option 3)

5

This is incorrect 

Option 4)

6

This is incorrect 

Posted by

Aadil

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