To Iterate or Not to Iterate? (Part 3)

Calculus Level 5

\[\large{2 + \cos(x)=0}\]

Suppose that \(x\) is a complex number in general, with a form \(A+Bi\) (where \(i=\sqrt{-1})\).

Find the solution (\(x)\) to the above equation with the minimum value of \(\sqrt{A^{2}+B^{2}}\).

Enter the corresponding value of \(\sqrt{A^{2}+B^{2}}\) to three decimal places.

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