I'm in Limbo

Algebra Level 5

iii...\LARGE { i }^{ { i }^{ i^{.^{.^{.}}} } }

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

Find the value of A2+B2{ A }^{ 2 }+{ B }^{ 2 } to 3 decimal places.

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