The least positive integer $n$ for which $\left( \frac{1 + i}{1 - i} \right)^{n}$ is real, is

Question

Dr. Abubacker · Accepted Answer

(a)
$\frac{1 + i}{1 - i} = \frac{(1 + i)^{2}}{1 - i^{2}} = \frac{2i}{2} = i$
So, $\left( \frac{1 + i}{1 - i} \right)^{n} = (i)^{n}\  \Rightarrow \ n = 2$

Q. The least positive integer $n$ for which $\left( \frac{1 + i}{1 - i} \right)^{n}$ is real, is

Explanation

Reviewed by Dr. Abubacker

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