If are th roots of unity

MATHEMATICS · Subjective · IB Diploma Programme · Mathematics: Analysis and Approaches · Number and Algebra · Number and Algebra

Problem

1, \omega, \omega^2, \dots, \omega^{n-1}

are

n

th roots of unity, find the value of

(9 - \omega)(9 - \omega^2) \dots (9 - \omega^{n-1})