Let w ≠ 1 be a cube root of unity and a, b, c are integers then minimum value of ∣∣a + bw + cw2∣∣2 is:
Question
Solution 1
The cube roots of unity are 1, w, and w^2, where w = -1/2 + sqrt(3)i/2 and w^2 = -1/2 - sqrt(3)i/2. These are the solutions to the equation x^3 = 1.
The expression a + bw + cw^2 is a complex number, and its square magnitude is given by |a + bw + cw^2|^2 = (a + bw + cw^2)(a + bw^2 + cw) = a^2 + ab(w Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
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