1, 2, 3, _ ?

Algebra Level 4

$$x, y$$ and $$z$$ are complex numbers satisfying

$\begin{cases} x^1+y^1+z^1 & = 1\\ x^2 + y^2 + z^2 & = 2 \\ x^3 + y^3 + z^3 & = 3 \\ \end{cases}$

The value of $$x^4 + y^4 + z^4$$ can be expressed as $$\frac {a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers. What is the value of $$a +b$$?

This problem is proposed by Harshit.

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