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  \[\frac{{{i}^{592}}+{{i}^{590}}+{{i}^{588}}+{{i}^{586}}+{{i}^{584}}}{{{i}^{582}}+{{i}^{580}}+{{i}^{578}}+{{i}^{576}}+{{i}^{574}}}-1=\]

    A) \[-1\]

    B) - 2

    C) \[-3\]

    D) - 4

    Correct Answer: B

    Solution :

    \[\frac{{{i}^{584}}({{i}^{8}}+{{i}^{6}}+{{i}^{4}}+{{i}^{2}}+1)}{{{i}^{574}}({{i}^{8}}+{{i}^{6}}+{{i}^{4}}+{{i}^{2}}+1)}-1=\frac{{{i}^{584}}}{{{i}^{574}}}-1\] \[={{i}^{10}}-1=-1-1=-2\]

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