Complicated Complex Fractions

Algebra Level 5

Let \(x, y\) and \(z\) be complex numbers such that

\[x + y + z = 2\]

\[x^2 + y^2 + z^2 = 3\]

\[xyz = 4\].

Evaluate

\[|\frac {1}{xy + z - 1} + \frac {1}{yz + x - 1} + \frac {1}{zx + y - 1}|\]

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