若z^2+z+1=0,求(1+z)*(1+z^2)*(1+z^4)*(1+z^8 )…(1+z^1若z^2+z+1=0,求(1+z)*(1+z^2)*(1+z^4)*(1+z^8)…(1+z^1024)的值.

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若z^2+z+1=0,求(1+z)*(1+z^2)*(1+z^4)*(1+z^8 )…(1+z^1若z^2+z+1=0,求(1+z)*(1+z^2)*(1+z^4)*(1+z^8)…(1+z^1024)的值.

若z^2+z+1=0,求(1+z)*(1+z^2)*(1+z^4)*(1+z^8 )…(1+z^1若z^2+z+1=0,求(1+z)*(1+z^2)*(1+z^4)*(1+z^8)…(1+z^1024)的值.
若z^2+z+1=0,求(1+z)*(1+z^2)*(1+z^4)*(1+z^8 )…(1+z^1
若z^2+z+1=0,求(1+z)*(1+z^2)*(1+z^4)*(1+z^8
)…(1+z^1024)的值.

若z^2+z+1=0,求(1+z)*(1+z^2)*(1+z^4)*(1+z^8 )…(1+z^1若z^2+z+1=0,求(1+z)*(1+z^2)*(1+z^4)*(1+z^8)…(1+z^1024)的值.
∵z²+z+1=0,∴z=(-1±根号3)/2,∴z≠1.
(z-1)(z²+z+1)=0,即z³=1.
∴原式=(1-z)•(1+z)•(1+z²)•(1+z∧4)•••(1+z∧1024)/1—z
=(1-z∧2048)/1-z
=1-z²╱1-z=1+z=(1±根号3)/2.