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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2013

  • question_answer
        If\[{{\log }_{1/2}}\frac{|z{{|}^{2}}+2|z|+4}{2|z{{|}^{2}}+1}<0,\]then the region traced by z is

    A)  \[|z|<3\]                           

    B)  \[1<|z|<3\]

    C)  \[|z|>1\]                           

    D)  \[|z|<2\]

    Correct Answer: A

    Solution :

                    \[\because \]\[{{\log }_{1/2}}\frac{|z{{|}^{2}}+2|z|+4}{2|z{{|}^{2}}+1}<0={{\log }_{1/2}}1\] \[\Rightarrow \]               \[\frac{|z{{|}^{2}}+2|z|+4}{2|z{{|}^{2}}+1}<1\]                \[(\because base<1)\] \[\Rightarrow \]               \[|z{{|}^{2}}-2|z|-3<0\]                 \[(|z|+1)(|z|-3)<0\] \[\therefore \]  \[|z|<3\]


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