11th Class Mathematics Complex Numbers and Quadratic Equations Question Bank Critical Thinking

  • question_answer If \[(1+i)(1+2i)(1+3i).....(1+ni)=a+ib\], then        2.5.10....\[(1+{{n}^{2}})\]  is equal to  [Karnataka CET 2002; Kerala (Engg.) 2002]

    A) \[{{a}^{2}}-{{b}^{2}}\]

    B) \[{{a}^{2}}+{{b}^{2}}\]

    C) \[\sqrt{{{a}^{2}}+{{b}^{2}}}\]

    D) \[\sqrt{{{a}^{2}}-{{b}^{2}}}\]

    Correct Answer: B

    Solution :

    We have \[(1+i)(1+2i)(1+3i).....(1+ni)=a+ib\]           .....(i) Þ \[(1-i)(1-2i)(1-3i).....(1-ni)=a-ib\]       .....(ii) Multiplying (i) and (ii), we get \[2.5.....(1+{{n}^{2}})={{a}^{2}}+{{b}^{2}}\]

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