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

  • question_answer
    If \[{{z}_{1}},{{z}_{2}}{{z}_{3}},{{z}_{4}}\]are the roots of the equation \[{{z}^{4}}=1\], then the value of  \[\sum\limits_{i=1}^{4}{z_{i}^{3}}\]is  [Kurukshetra CEE 1996]

    A) 0

    B) 1

    C) \[i\]

    D) \[1+i\]

    Correct Answer: A

    Solution :

    \[{{z}_{1}}=1,{{z}_{2}}=i,{{z}_{3}}=-1,{{z}_{4}}=-i\] \ \[{{1}^{3}}+{{(i)}^{3}}+{{(-1)}^{3}}+{{(-i)}^{3}}=0\].


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