if 1, omega, omega ² are the cube roots of unity, then prove the following: (1 + omega) (1 + omega²) (1 + omega^7) (1 + omega^8) =1
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Answer:- Omega=w
=>1+w+w^2=0
=>1+w=(-w^2)
=>1+w^2=(-w)
=>w^3=1
(1+w) (1+w^2) (1+w^7) (1+w^8)=1
LHS
=>(-w^2) (-w) (1+ w^6•w) (1+w^6•w^2)
=>(-w^2) (-w) (1+ (w^3)^2•w) (1+(w^3)^2•w^2)
=>(-w^2) (-w) (1+w) (1+w^2)
=>(w^3) (-w^2) (-w)
=>(w^3) (w^3)
=>1•1
=>1=RHS
Step-by-step explanation:
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