To Iterate or Not to Iterate? (Part 2)

Calculus Level 5

\[\large{x + e^{x}=0}\]

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 \(\sqrt{A^{2}+B^{2}}\), subject to the constraint that \((B\not=0)\).

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


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