Question

Let \( \omega (\neq 1) \) be a cubic root of unity. Then the minimum value of the set \( \{ |a + b\omega + c\omega^2|^2 : a, b, c \) are distinct non-zero integers \( \} \) equals:

• A. \( 15 \)
• B. \( 5 \)
• C. \( 3 \)
• D. \( 4 \)

Hint:

Remember the fundamental properties of cubic roots of unity, especially \( 1 + \omega + \omega^2 = 0 \) and \( \omega^3 = 1 \), as they are crucial for simplifying expressions involving \( \omega \).