# Imaginary Powerhouse $$(i)$$

Number Theory Level 3

$\Large n={1^{2^{3}}+4^{5^{6^{7^{8}}}} \times 9^{10^{11^{...^{14^{15}}}}} +16^{17^{18 ^{...^{24}}}} \times25^{26^{...^{34^{35}}}}}$

For $$n$$ as defined above, what is the value of $$i^{n}$$?

Clarification: $$i=\sqrt{-1}$$ denotes the imaginary unit.

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