Problem: If w is one of the imaginary roots of the equation x3=1, then the product (1−w+ w2)(1+w−w2) is equal to
Answer Choices:
A. 4
B. w
C. 2
D. w2
E. 1
Solution:
Factoring the given equation x3−1=0 gives (x−1)(x2+x+1)=0. The imaginary root w satisfies w2+w+1=0. Hence 1+w2=−w,1+w=−w2 ∴(1−w+w2)(1+w−w2)=(−2w)(−2w2)=4w3=4 because w3=1.