Complex Cosine

Algebra Level 4

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

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

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