# Really finding roots

Algebra Level 5

$\begin{eqnarray} a+b+c &=& abc \\ ab +bc + ca &=& 1 \\ a^2+b^2 + c^2 &=& 1 \\ \end{eqnarray}$

Let $$a,b,c$$ be complex numbers satisfying the system of equations above. What is the value of $$|a|^2+|b|^2+|c|^2$$?

×