A Complex Problem

Algebra Level 5

Let \(a, b, c\) be 3 complex numbers such that \(|a| = |b| = |c| = 1\) and \(\dfrac{a^2}{bc}+ \dfrac{b^2}{ac} + \dfrac{c^2}{ab} + 1 = 0\) . If \(|a + b + c|\) can take values that equal \(p\) and \(q\), then find the value of \(p+q\) .