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$\LARGE { i }^{ { i }^{ i^{.^{.^{.}}} } }$

For $i = \sqrt{-1}$, the value of the infinitely nested exponent above is equal to $A + Bi$ for real values $A$ and $B$.

Find the value of ${ A }^{ 2 }+{ B }^{ 2 }$ to 3 decimal places.

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