$c$ is a complex number that satisyfing $(c+\frac{1}{c}+1)(c+\frac{1}{c}) = 1$ Let $c$ is complex-number satisfying :
$(c+\frac{1}{c}+1)(c+\frac{1}{c}) = 1$
So, how could i get
$(3c^{100}+\frac{2}{c^{100}}+1)(c^{100}+\frac{2}{c^{100}}+3)$ ?

HINT:
On simplification, $c^4+c^3+c^2+c+1=0$
Clearly,  $c\ne1$ 
Multiply either sides the $(c-1),$ we get $c^5-1=(c-1)\cdot0=0$
$\implies c^5=1\implies c^{100}=(c^5)^{20}=1$
