Hello i have some problems with solving two things connected with complex numbers:

1)

$\displaystyle |i^{\hat{z}}|=e$

I tried with logarythming both sides, so i get:

$\displaystyle \hat{z}=\frac{1}{ln i}=\frac{1}{i ( \frac{ \pi}{2}+ 2k \pi)}$

and here i stuck...

2)

$\displaystyle arg( i^{ \hat{z}})= \frac{ \pi}{2}$

Here i even do not have idea how to start