Imaginary Powerhouse \((i)\)

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

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

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

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