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

  • question_answer
    If \[\omega \] is an nth root of unity, other than unity, then the value of \[1+\omega +{{\omega }^{2}}+...+{{\omega }^{n-1}}\] is     [Karnataka CET 1999]

    A) 0

    B) 1

    C) \[-1\]

    D) None of these

    Correct Answer: A

    Solution :

    \[1+\omega +{{\omega }^{2}}+.....+{{\omega }^{n-1}}=\left( \frac{{{\omega }^{n}}-1}{\omega -1} \right)=0\], \[(\because {{\omega }^{n}}=1)\]


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