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

  • question_answer \[1+{{i}^{2}}+{{i}^{4}}+{{i}^{6}}+.....+{{i}^{2n}}\]is [EAMCET 1980]

    A) Positive

    B) Negative

    C) Zero

    D) Cannot be determined

    Correct Answer: D

    Solution :

    \[S=1+{{i}^{2}}+{{i}^{4}}+.....+{{i}^{2n}}=1-1+1-1+......+{{(-1)}^{n}}\] Obviously it depends on\[n\]. Hence cannot be determined unless \[n\] is known.

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