# 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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