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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Square root, Representation and Logarithm of complex numbers

  • question_answer
    The number of non-zero integral solutions of the equation \[|1-i{{|}^{x}}={{2}^{x}}\] is

    A) Infinite

    B) 1

    C) 2

    D) None of these

    Correct Answer: D

    Solution :

    Since  \[1-i=\sqrt{2}\left\{ \cos \frac{\pi }{4}-i\sin \frac{\pi }{4} \right\},|1-i|=\sqrt{2}\] \[\therefore \]\[|1-i{{|}^{x}}={{2}^{x}}\]Þ\[{{(\sqrt{2})}^{x}}={{2}^{x}}\]Þ \[{{2}^{x/2}}={{2}^{x}}\] Þ \[\frac{x}{2}=x\]Þ \[x=0\] Therefore, the number of non-zero integral solutions is nil or zero.


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