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

  • question_answer
    If \[z=3+5i,\,\,\text{then }\,{{z}^{3}}+\bar{z}+198=\] [EAMCET 2002]

    A) \[-3-5i\]

    B) \[-3+5i\]

    C) \[3+5i\]

    D) \[3-5i\]

    Correct Answer: B

    Solution :

    \[z=3+5i\], \[\bar{z}=3-5i\] \[\Rightarrow \,\]\[{{z}^{3}}={{(3+5i)}^{3}}={{3}^{3}}+{{(5i)}^{3}}+3.3.5i\,(3+5i)\]            \[=-198+10i\] Hence, \[{{z}^{3}}+\bar{z}+198=10\,i-198+3-5\,i+198=3+5\,i\].


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