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JEE Main & Advanced JEE Main Online Paper (Held on 9 April 2013)

  • question_answer
                    If \[{{Z}_{1}}\ne O\] and \[{{Z}_{2}}\]  be two complex numbers such that  \[\frac{{{Z}_{2}}}{{{Z}_{1}}}\] is a purely imaginary number, then \[\left| \frac{2{{Z}_{1}}+3{{Z}_{2}}}{2{{Z}_{1}}-3{{Z}_{2}}} \right|\] is equal to:               JEE Main Online Paper (Held On 09 April 2013)

    A)                 2                

    B)                 5                

    C)                 3                

    D)                 1                

    Correct Answer: D

    Solution :

                    Given, \[\frac{{{z}_{2}}}{{{z}_{1}}}\] is a purely imaginary i.e., \[ni\]                 Now, \[\left| \frac{2+3\frac{{{z}_{2}}}{{{z}_{1}}}}{2-3\frac{{{z}_{2}}}{{{z}_{1}}}} \right|=\left| \frac{2+3ni}{2-3ni} \right|=\frac{\sqrt{4+9{{n}^{2}}}}{4+9{{n}^{2}}}=1\]                


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