Unformatted text preview: (i) ( 5 marks ) n X k =1 z k ! = n X k =1 z k (ii) ( 5 marks ) ( z 1 z 2 ··· z n ) = z 1 z 2 ··· z n 2. ( 10 marks ) Let N be a ﬁxed positive integer. Consider the polynomial P ( z ) := N X k =0 a k z k , z ∈ C , where every a k , 0 ≤ k ≤ N , is a real number. Prove that a complex number ω is a root of P if and only if ω is also a root of P ; that is, prove that P ( ω ) = 0 if and only if P ( ω ) = 0....
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 Fall '08
 Staff
 Addition, Complex number, positive integer

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