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JEE Main & Advanced Sample Paper JEE Main Sample Paper-28

  • question_answer
    If \[{{z}_{1}}\ne 0\] 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

    A)  1

    B)  3

    C)  5

    D)  2

    Correct Answer: A

    Solution :

    Let  \[\frac{{{z}_{2}}}{{{z}_{1}}}=i\lambda \]              \[\left| \frac{2{{z}_{1}}+3{{z}_{2}}}{2{{z}_{1}}-3{{z}_{2}}} \right|=\left| \frac{2+3i{{\lambda }_{2}}}{2-3i{{\lambda }_{2}}} \right|=1\]


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