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 \[{{(1+i)}^{6}}+{{(1-i)}^{6}}\] is  [RPET 2002]

    A) 0

    B) 27

    C) 26

    D) None of these

    Correct Answer: A

    Solution :

    \[{{\left( 1+i \right)}^{6}}+{{(1-i)}^{6}}={{[{{(1+i)}^{2}}]}^{3}}+{{[{{(1-i)}^{2}}]}^{3}}\] \[=\,{{(2i)}^{3}}+{{(-2i)}^{3}}\]\[=(8-8){{i}^{3}}=0\].

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