Let f(x)=1+2 x+3 x^{2}+4 x^{3}+5 x^{4} and let \zeta=e^{2 \pi i / 5}=\cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5}. Find the value of the following expression:
f(\zeta) f\left(\zeta^{2}\right) f\left(\zeta^{3}\right) f\left(\zeta^{4}\right)
Let f(x)=1+2 x+3 x^{2}+4 x^{3}+5 x^{4} and let \zeta=e^{2 \pi i / 5}=\cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5}. Find the value of the following expression:
f(\zeta) f\left(\zeta^{2}\right) f\left(\zeta^{3}\right) f\left(\zeta^{4}\right)