Question

If 1,\omega ,\omega ^{2}, are cube roots of unity, show that \left ( 2-\omega \right )\left ( 2-\omega ^{2} \right )\left ( 2-\omega ^{23} \right )=49.

22 Apr 2024
Answer :
Word Count : 386
To solve this problem numerically, we need to use the properties of the cube roots of unity. Let the cube roots of unity be denoted as \( 1, \omega, \omega^2 \). These roots satisfy the following equations: 1. \( \omega^3 = 1 \) 2. \( 1 + \omega + \omega^2 = 0 \) We are asked to show that: \[ (2 - \omega)(2 - _____ __________ ___ ______ _____ _________ _______ ________ ___ ____ _____ _________.
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