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Imaginary root w

Source: 1971 AHSME Problem 22

April 22, 2014
AMC

Problem Statement

If ww is one of the imaginary roots of the equation x3=1x^3=1, then the product (1−w+w2)(1+w−w2)(1-w+w^2)(1+w-w^2) is equal to
<spanclass=′latex−bold′>(A)</span>4<spanclass=′latex−bold′>(B)</span>w<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>w2<spanclass=′latex−bold′>(E)</span>1<span class='latex-bold'>(A) </span>4\qquad<span class='latex-bold'>(B) </span>w\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>w^2\qquad <span class='latex-bold'>(E) </span>1
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