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

    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) \[\Rightarrow \,\,(a-ib)(c-id)(e-if)(g-ih)=A-iB\]   ...(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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