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JEE Main & Advanced JEE Main Paper (Held On 11-Jan-2019 Morning)

  • question_answer
    Let\[{{\left( -2-\frac{1}{3}i \right)}^{3}}=\frac{x+iy}{27}(i=\sqrt{-1}),\]x and y are real numbers, then y - x equals [JEE Main Online Paper (Held On 11-Jan-2019 Morning]

    A) \[-91~~~\]                              

    B)               \[-85~~\]

    C)               85                                            

    D)               91

    Correct Answer: D

    Solution :

    Given, \[{{\left( -2-\frac{1}{3}i \right)}^{3}}=\frac{x+iy}{27}\] \[\Rightarrow \]\[\frac{-{{(6+i)}^{3}}}{27}=\frac{x+iy}{27}\] \[\Rightarrow \]\[(198+107i)=x+iy\] \[\Rightarrow \]\[x=-197\]and\[y=-107\] \[\therefore \]\[y-x=198-107=91\]


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