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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 \[(a+ib)(c+id)(e+if)(g+ih)\]\[=A+iB,\] then \[({{a}^{2}}+{{b}^{2}})({{c}^{2}}+{{d}^{2}})({{e}^{2}}+{{f}^{2}})({{g}^{2}}+{{h}^{2}})\] = [MNR 1989]

    A) \[{{A}^{2}}+{{B}^{2}}\]

    B) \[{{A}^{2}}-{{B}^{2}}\]

    C) \[{{A}^{2}}\]

    D) \[{{B}^{2}}\]

    Correct Answer: A

    Solution :

    \[(a+ib)(c+id)(e+if)(g+ih)=A+iB\] .....(i) Þ \[(a-ib)(c-id)(e-if)(g-ih)=A-iB\] ......(ii) Multiplying (i) and (ii), we get \[({{a}^{2}}+{{b}^{2}})({{c}^{2}}+{{d}^{2}})({{e}^{2}}+{{f}^{2}})({{g}^{2}}+{{h}^{2}})={{A}^{2}}+{{B}^{2}}\]


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