Deep root

Algebra Level 5

The real solution of the equation below can be expressed as \(x=z+z^{*}\), where \(z\) is a complex number, with \(|z|=1\). If \(\arg{z}=\frac{a}{b}\pi\), where \(a\) and \(b\) are co-prime, find \(b-a\). \[x=\sqrt{2+\sqrt{2-\sqrt{2+x}}}\]

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