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