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

  • question_answer If \[n\] is a positive integer, then which of the following relations is false

    A) \[{{i}^{4n}}=1\]

    B) \[{{i}^{4n-1}}=i\]

    C) \[{{i}^{4n+1}}=i\]

    D) \[{{i}^{-4n}}=1\]

    Correct Answer: B

    Solution :

    We know that \[{{i}^{2}}=-1\] Þ \[{{({{i}^{2}})}^{2}}={{(-1)}^{2}}=1\Rightarrow \,\,\,\,{{i}^{4n}}={{1}^{n}}\] and therefore \[{{i}^{4n-1}}=-i\]

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