# 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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