Let zzz be a complex number such that z+1z=2cosθz + \frac{1}{z} = 2\cos\thetaz+z1=2cosθ. What is zn+1znz^n + \frac{1}{z^n}zn+zn1?
2cos(nθ)2\cos(n\theta)2cos(nθ)
2isin(nθ)2i\sin(n\theta)2isin(nθ)
2cosn(θ)2\cos^n(\theta)2cosn(θ)
2insin(nθ)2i^n\sin(n\theta)2insin(nθ)