# Complex Numbers $x,y,z$ Find $x^{2007}+y^{2007}+z^{2007}$

Let $x,y,z$ be complex numbers such that

$$x+y+z = x^{5}+y^{5}+z^{5} = 0, \hspace{10pt} x^3+y^3+z^3=2$$

Find all possible values of

$$x^{2007}+y^{2007}+z^{2007}$$

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