If Z ^ 2 + Z + 1 = 0, find (1 + Z) * (1 + Z ^ 2) * (1 + Z ^ 4) * (1 + Z ^ 8) （1+z^1 If Z ^ 2 + Z + 1 = 0, find (1 + Z) * (1 + Z ^ 2) * (1 + Z ^ 4) * (1 + Z ^ 8) ）… (1 + Z ^ 1024)

∵ Z & # 178; + Z + 1 = 0, ∵ z = (- 1 ± root sign 3) / 2, ∵ Z ≠ 1
(Z-1) (Z & # 178; + Z + 1) = 0, that is Z & # 179; = 1
The original formula = (1-z) & #8226; (1 + Z) & #8226; (1 + Z & #178;) & #8226; (1 + Z Λ 4) & #8226; & #8226; (1 + Z Λ 1024) / 1-z
=（1-z∧2048）/1-z
=1-z & # 178; / 1-z = 1 + Z = (1 ± root 3) / 2