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 \[\omega \] is a non real cube root of unity, then \[(a+b)\] \[(a+b\omega )\] \[(a+b{{\omega }^{2}})\] is [Kerala (Engg.) 2002]

    A) \[{{a}^{3}}+{{b}^{3}}\]

    B) \[{{a}^{3}}-{{b}^{3}}\]

    C) \[{{a}^{2}}+{{b}^{2}}\]

    D) \[{{a}^{2}}-{{b}^{2}}\]

    Correct Answer: A

    Solution :

    \[(a+b)\,(a+b\omega )\,(a+b{{\omega }^{2}})\] \[=\,(a+b)\,({{a}^{2}}+ab\,(\omega +{{\omega }^{2}})+{{b}^{2}}{{\omega }^{3}})\] \[=(a+b)\,({{a}^{2}}-ab+{{b}^{2}})\,=\,{{a}^{3}}+{{b}^{3}}\].


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