Complex Cosine

Algebra Level 4

The equation $$\cos { (z) }=4$$ has two solutions, where $$z$$ is purely imaginary.

If the expression $$\large \displaystyle{ e }^{ z / i }$$ can be expressed in simplest form as $$a \pm \sqrt { b }$$, where $$b$$ is square-free, find the value of $$a+b$$.

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