2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Complex Numbers and Quadratic Equations

JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank De Moivre's theorem and Roots of unity

  • question_answer
    If \[1,\,\omega ,\,{{\omega }^{2}}\] are the roots of unity, then \[{{(1-2\omega +{{\omega }^{2}})}^{6}}\] is equal to [Pb. CET 2001]

    A) 729

    B) 246

    C) 243

    D) 81

    Correct Answer: A

    Solution :

    \[{{(1-2\omega +{{\omega }^{2}})}^{6}}\] = \[{{(1+{{\omega }^{2}}-2\omega )}^{6}}\] = \[{{(-\omega -2\omega )}^{6}}={{(-3\omega )}^{6}}\] \[={{(-3)}^{6}}{{({{\omega }^{3}})}^{2}}\]     [Since \[1+\omega +{{\omega }^{2}}=0,\,{{\omega }^{3}}=1\]] = 729.


You need to login to perform this action.
You will be redirected in 3 sec spinner