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Value of (a + b omega + c omega^2)^n using 1 + omega + omega^2 = 0

This type of question, asked 2 times: 10 May 2023 S1, 15 May 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    10 May 2023 S1

    134
    If w=−1+i32w=\frac{-1+i\sqrt{3}}{2}, where i=−1i=\sqrt{-1}, then the value of (3+w+3w2)4(3+w+3w^2)^4 is

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  2. Question 2

    15 May 2026 S2

    56
    If ω\omega is a complex cube root of unity, then the value of the expression (1−ω+ω2)7+(1+ω−ω2)7(1 - \omega + \omega^2)^7 + (1 + \omega - \omega^2)^7 is equal to...

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