Complicated Expression

Algebra Level 5

Let \(x\) be a solution to the equation \(x^2+x+2014=0\).

Find the value of \[\lim\limits_{n\to \infty} \sqrt[\Large n]{\prod_{i=1}^{2n}\left|\dfrac{x^i}{2014^{\frac{i-1}{2}}}+1\right|}.\]

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