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 \[{{i}^{n}}+{{i}^{n+1}}+{{i}^{n+2}}+{{i}^{n+3}}\,,\,(n\in N)\] is [RPET 2001]

    A) 0

    B) 1

    C) 2

    D) None of these

    Correct Answer: A

    Solution :

    \[{{i}^{n}}+{{i}^{n+1}}+{{i}^{n+2}}+{{i}^{n+3}}={{i}^{n}}[1+i+{{i}^{2}}+{{i}^{3}}]\]\[=\,{{i}^{n}}[1+i-1-i]=0\].


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