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

  • question_answer
    The value of (8)1/3 is [RPET 2003]

    A) \[-1+i\sqrt{3}\]

    B) \[-1-i\sqrt{3}\]

    C) 2

    D) All of these

    Correct Answer: D

    Solution :

    \[{{(8)}^{1/3}}=x\Rightarrow {{x}^{3}}-8=0\] Þ \[(x-2)\,({{x}^{2}}+2x+4)=0\]. Þ \[x=2,\,2\omega ,\,2{{\omega }^{2}}\] or \[x=2,\,-1+i\sqrt{3},\,-1-i\sqrt{3}\].


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