I think we are to find the principle value of $\displaystyle i^{2i}$.
$\displaystyle
i^{2i} = \exp \left( {2i\text{Log}(i)} \right) = \exp \left( {(2i)\left( {i\frac{\pi }{2}} \right)} \right) = ?$
I think we are to find the principle value of $\displaystyle i^{2i}$.
$\displaystyle
i^{2i} = \exp \left( {2i\text{Log}(i)} \right) = \exp \left( {(2i)\left( {i\frac{\pi }{2}} \right)} \right) = ?$
The principle value of $\displaystyle z^w=\exp\left(w\cdot\text{Log}(z)\right)$.
Now $\displaystyle \text{Arg}(i)=\frac{\pi}{2}$ and $\displaystyle |i|=1$ so $\displaystyle \ln(1)=0$
I think we are to find the principle value of $\displaystyle i^{2i}$.
$\displaystyle
i^{2i} = \exp \left( {2i\text{Log}(i)} \right) = \exp \left( {(2i)\left( {i\frac{\pi }{2}} \right)} \right) = ?$