JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Conjugate, Modulus and Argument of complex number

  • question_answer
    For any complex number \[z,\bar{z}=\left( \frac{1}{z} \right)\]if and only if  [RPET 1985]

    A) \[z\] is a pure real number

    B) \[|z|=1\]

    C) \[z\]is a pure imaginary number

    D) \[z=1\]

    Correct Answer: B

    Solution :

    Given that \[\overline{z}=\frac{1}{z}\Rightarrow z\overline{z}=1\] Þ \[|z{{|}^{2}}=1\Rightarrow |z|=1\]


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