If 1, 𝜔,𝜔2 are cube roots of unity, show that(2 – 𝜔) (2 – 𝜔2) (2 – 𝜔19) (2 – 𝜔23) = 49
Question
Solution 1
Sure, let's solve this step by step.
Step 1: We know that the cube roots of unity are 1, 𝜔, 𝜔². These are the solutions to the equation x³ = 1.
Step 2: We also know that 𝜔³ = 1 and 𝜔ⁿ = 𝜔^(n mod 3) for any integer n.
Step 3: Using the above property, we can simplify 𝜔¹⁹ and 𝜔²³ as follows:
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s:
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