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Algebra Level 5

Let x,yx, y and z z be complex numbers such that

{x=y=z,xyz=64,xy+yz+zx=24. \begin{cases} |x|=|y|=|z|, \\ xyz=64, \\ xy+yz+zx=24.\\ \end{cases}

Find the value of x+y+z|x+y+z|.

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