• # 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

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