Complex Cosine

Algebra Level 5

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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