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JEE Main & Advanced Sample Paper JEE Main Sample Paper-27

  • question_answer
    If \[{{z}_{1}},{{z}_{2}}\] and \[{{z}_{3}},{{z}_{4}}\] are 2 pairs of complex conjugate numbers, then arg \[\left( \frac{{{z}_{i}}}{{{z}_{4}}} \right)\] arg \[\left( \frac{{{z}_{2}}}{{{z}_{3}}} \right)\]equals

    A)  \[\frac{\pi }{2}\]                                   

    B)  0

    C)  \[\frac{3\pi }{2}\]                                 

    D)  \[\pi \]

    Correct Answer: B

    Solution :

    \[\arg \left( \frac{{{z}_{1}}}{{{z}_{4}}} \right)+\arg \,\left( \frac{{{z}_{2}}}{{{z}_{3}}} \right)\] \[\Rightarrow \,\arg \left( \frac{{{z}_{1}}{{z}_{2}}}{{{z}_{3}}{{z}_{4}}} \right)\] = arg (some positive real no.) = 0


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