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 least positive integer \[n\] which will reduce \[{{\left( \frac{i-1}{i+1} \right)}^{n}}\] to a real number, is [Roorkee 1998]

    A) 2

    B) 3

    C) 4

    D) 5

    Correct Answer: A

    Solution :

    \[{{\left( \frac{i-1}{i+1}\times \frac{i-1}{i-1} \right)}^{n}}={{\left( \frac{-2i}{-2} \right)}^{n}}={{i}^{n}}\] Hence, to make the real number the least positive integer is 2.

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