Question

Let \( \omega (\ne 1) \) be a cube root of unity. Then the minimum value of the set \[ \left\{ |a + b\omega + c\omega^2|^2 : a,b,c \text{ are distinct non-zero integers} \right\} \] equals:

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

Hint:

For cube roots of unity: \begin{itemize} \item Use \( 1+\omega+\omega^2=0 \). \item Modulus simplifies to symmetric quadratic form. \end{itemize}

Answer 1

The Correct Option is B