Find all the solutions of $e^z=i$ Find all the solutions of $e^z=i$

I don't know where to start.

I want to do $z=\ln(i)$, but have no idea where that would lead me.

Thanks in advance.
Hint: write $z=x+iy$ and solve the real and imaginary parts separately: $$e^{x+iy} = e^x (\cos y + i \sin y) = 0 + i$$



Adding more detail:

$$\begin{cases}e^x \cos y = 0 \\ e^x \sin y = 1\end{cases}$$
Noting that $e^x &gt; 0$ for any $x$,
$$e^x \cos y = 0 \implies \cos y = 0 \implies y = \pi/2 + k \implies \sin y = \pm 1$$
Again, using the fact that $e^x&gt;0$, this implies
$$\sin y = 1 \implies \begin{cases}x=0 \\ y=\pi/2 + 2\pi k\end{cases}$$
Write $i$ as ${\large e^{i\left(\dfrac\pi2 + 2n\pi\right)}}$. Then compare the powers on both sides, take LCM and boom!