If and are the th roots of unity

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

Problem

If

n \ge 3

and

1, \alpha_1, \alpha_2, \alpha_3, \dots, \alpha_{n-1}

are the

n

th roots of unity, then find the value of

\sum_{1 \le i < j \le n-1} \alpha_i \alpha_j.

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