Solving Euler's identity

Question

When I first saw the Euler's identity $$e^{\theta i}=\cos(\theta)+i\sin(\theta)$$ I realized $$x=e^{\frac{πx}{2}}$$ must have a complex solution $x=i$. However, although I know the solution, I'm unable to find the way that leads to it. By some simple changes I've achieved $$x=-\frac{2}{π}W(-\frac{π}{2})$$. So I guess the equation has more solutions since the one I wrote is definitely not $i$. I searched a lot on the Internet but couldn't find anything that would show the approach to get exactly $x=i$. There might be something obvious I'm missing but I would be really happy if anyone could give me a hint how to mathematically get $x=i$ from that equation $x=e^{\frac{πx}{2}}$.