i-1-i-xi-i-x-x-

Question Number 153682 by EDWIN88 last updated on 09/Sep/21

{(\sqrt[i]{i})}^{x i} = i^{x}

x = ?

Answered by MJS_new last updated on 09/Sep/21

lhs i = e^{i \frac{π}{2}} \Rightarrow \sqrt[i]{i} = e^{\frac{π}{2}} \Rightarrow {(\sqrt[i]{i})}^{i x} = e^{i \frac{x π}{2}}

rhs i^{x} = e^{i \frac{x π}{2}}

\Rightarrow x \in C

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