z = \left(\frac{i - 1}{i + 1}\right)^6=\frac{\sqrt{2}^6\cdot(\cos\frac{3\pi}{2}+i\sin\frac{3\pi}{2})}{\sqrt{2}^6\cdot(\cos\frac{9\pi}{2}+i\sin\frac{9\pi}{2})}=\frac{-8i}{8i}=-1