Q. The smallest positive integer $n$ for which $\left( \frac{1 + i}{1 - i} \right)^{n} = 1$, is
A) $n = 8$
B) $n = 12$
C) $n = 16$
D) None of these
Explanation
(d)
$\frac{1 + i}{1 - i} = \frac{(1 + i)^{2}}{1 - i^{2}} = i$
Since, $\left( \frac{1 + i}{1 - i} \right)^{n} = 1\ \ \ \Rightarrow \ \ \ i^{n} = 1$
Hence, smallest positive integer is 4
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.