# 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 $$p+q$$ .

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