JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Integral power of iota, Algebraic operations and Equality of complex numbers

  • question_answer
    If \[\]\[x+\frac{1}{x}=2\cos \theta ,\] then x is equal to [RPET 2001]

    A) \[\cos \theta +i\,\sin \theta \]

    B) \[\cos \theta -i\,\sin \theta \]

    C) \[\cos \theta \pm i\,\sin \theta \]

    D) \[\sin \theta \pm i\,\cos \theta \]

    Correct Answer: C

    Solution :

    \[x+\frac{1}{x}=2\cos \theta \]\[\Rightarrow \,{{x}^{2}}-2x\cos \theta +1=0\] Þ \[x=\frac{2\cos \theta \pm \sqrt{4{{\cos }^{2}}\theta -4}}{2}\] Þ \[x=\cos \theta \pm i\sin \theta \].

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