Question
The smallest positive integral value of 'n' such that $\left[\frac{1 + \sin\frac{\pi}{8} + i \cos\frac{\pi}{8}}{1 + \sin\frac{\pi}{8} - i \cos\frac{\pi}{8}}\right]^n$ is purely imaginary when $n = $
The smallest positive integral value of 'n' such that $\left[\frac{1 + \sin\frac{\pi}{8} + i \cos\frac{\pi}{8}}{1 + \sin\frac{\pi}{8} - i \cos\frac{\pi}{8}}\right]^n$ is purely imaginary when $n = $