# Again a Complex Number System

Algebra Level 5

Let $$a, b, c$$ be complex numbers satisfying $a + b +c = abc = 1$

and $\dfrac{ab+bc+ac}{3} = \dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}$

The sum of absolute values of all possible $$ab + ac + bc$$ can be written as $$\dfrac{\sqrt{n}}{m}$$ , where $$n$$ and $$m$$ are positive coprime integers. What is the value of $$n + m$$ ?

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