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JEE Main & Advanced Sample Paper JEE Main Sample Paper-21

  • question_answer
    If \[|{{z}_{i}}|=2\] and \[(1-i){{z}_{2}}+(1-i){{\overrightarrow{z}}_{_{2}}}=8\sqrt{2},\] then the minimum value of \[|{{z}_{1}}-{{z}_{2}}|\] equals \[[Note:i=\sqrt{-1}.]\]

    A)  4                                

    B)  3

    C)  2                                

    D)  1

    Correct Answer: C

    Solution :

    \[|{{z}_{1}}|=2,\] a circle of radius 2 and \[(1-i)\,{{z}_{2}}+(1+i)\,{{\overline{z}}_{2}}=8\sqrt{2}\] \[\Rightarrow \] a straight line \[x+y=4\sqrt{2}\] \[\therefore \] AB is minimum along a line y = x \[A=(\sqrt{2},\,\,\sqrt{2}),B\,=(2\sqrt{2},\,\,2\sqrt{2})\] \[\therefore \,\,AB=\sqrt{{{\left( 2\sqrt{2}-\sqrt{2} \right)}^{2}}\,+{{\left( 2\sqrt{2}\,-\sqrt{2} \right)}^{2}}}\] \[=\sqrt{2+2}=\sqrt{4}=2\]


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