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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  \[x=a,y=b\omega ,z=c{{\omega }^{2}}\], where \[\omega \] is a complex cube root of unity, then \[\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=\] [AMU 1983]

    A) 3

    B) 1

    C) 0

    D) None of these

    Correct Answer: C

    Solution :

    Given that \[x=a,y=b\omega ,z=c{{\omega }^{2}}\] Then \[\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=\frac{a}{a}+\frac{b\omega }{b}+\frac{c{{\omega }^{2}}}{c}=1+\omega +{{\omega }^{2}}=0\]


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