(1+i)^{k}\cdot{(1+i)}=2^{\frac{k}{2}}{\Big (\cos{\frac{k\pi}{4}+i\sin{\frac{k\pi}{4}}}\Big )}\cdot{2^{\frac{1}{2}}\Big (\cos{\frac{\pi}{4}}+i\sin{\frac{\pi}{4}}\Big)}