• # 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) $\left( \frac{3-4ix}{3+4ix} \right)=$

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