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

  • question_answer
    \[{{\left\{ \frac{2i}{1+i} \right\}}^{2}}=\] [BIT Ranchi 1992]

    A) 1

    B) \[2i\]

    C) \[\alpha -i\beta \,(\alpha ,\beta \,\text{real),}\]

    D) \[\left( \frac{3-4ix}{3+4ix} \right)=\]

    Correct Answer: B

    Solution :

    \[{{\left[ \frac{2i}{1+i} \right]}^{2}}={{\left[ \left( \frac{2i}{1+i} \right)\,\left( \frac{1-i}{1-i} \right) \right]}^{2}}={{(i+1)}^{2}}={{i}^{2}}+1+2i=2i\].

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