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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Self Evaluation Test - Complex Numbers and Quadratic Equations

  • question_answer
    If z and \[\omega \] are two non-zero complex numbers such that \[\left| z\omega  \right|=1\] and \[Arg(z)-Arg(\omega )=\frac{\pi }{2},\]then \[\bar{z}\omega \] is equal to

    A) \[-i\]                 

    B) \[1\]   

    C) \[-1\]    

    D) \[i\]

    Correct Answer: C

    Solution :

    Consider \[|\bar{z}\omega ||\bar{z}||\omega |=|z||\omega |=|z\omega |=1\] Consider \[Arg\,(\bar{z}\omega )=\arg (\bar{z})+arg(\omega )=-arg(z)+arg\omega \] \[=-\frac{\pi }{2}\,\,\,\therefore \,\,\bar{z}\omega =-1\]


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