Let be a cube root of unity

MATHEMATICS · Subjective · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

Let

w \neq 1

be a cube root of unity. Then, the minimum of the set

\{|a + b\omega + c\omega^2|^2 \mid a, b, c \text{ distinct non-zero integers}\}

equals ---