JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Integral power of iota, Algebraic operations and Equality of complex numbers

  • question_answer The value of \[{{(1+i)}^{8}}+{{(1-i)}^{8}}\] is  [RPET 2001; KCET  2001]

    A) 16

    B) - 16

    C) 32

    D) - 32

    Correct Answer: C

    Solution :

    \[\because \,{{(1+i)}^{2}}=\,1+{{i}^{2}}+2i=2i\] and \[{{(1-i)}^{2}}=1+{{i}^{2}}-2i=-2i\] \[\Rightarrow {{(1+i)}^{8}}+{{(1-i)}^{8}}={{(2i)}^{4}}+{{(-2i)}^{4}}\]\[={{2}^{4}}({{i}^{4}}+{{i}^{4}})\]                             \[={{2}^{5}}=32.\]

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