# I'm in Limbo

Algebra Level 5

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

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.

×