N^i

[Zolar V]

I'm trying to understand what it means to take a number \(n \) to the power of \( i \).

\[ F(x) = x^i     = x^{\sqrt{-1}} \]

 

I'm trying to understand visually what taking a number to a squareroot really does to it. Examine the behavior.   I want to be able to understand it visually as well as numerically.

I suppose it would be useful to also understand what a number \( n \) to a root \( \sqrt{a} \)  also means.
 

\[ G(y) = n ^ { \sqrt{y}}  ,  y \in \mathbb{Z}  \] 

 

Edited October 18, 2019 by Zolar V

[mathematic]

\( x^i=e^{iln(x)}=cos(ln(x))+isin(ln(x)) \)

Edited October 18, 2019 by mathematic
latex setup