A Complex Problem

Algebra Level 5

Let a,b,ca, b, c be 3 complex numbers such that a=b=c=1|a| = |b| = |c| = 1 and a2bc+b2ac+c2ab+1=0\dfrac{a^2}{bc}+ \dfrac{b^2}{ac} + \dfrac{c^2}{ab} + 1 = 0 . If a+b+c|a + b + c| can take values that equal pp and qq, then find the value of p+qp+q .

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