I have some issue with $\exp(j)$ and I'm not sure what is the origin of it.
On one side: $\exp(j*\pi) = -1$
On the other side I can write: $$\exp\left(j*(2\pi)*\tfrac 1 2\right) = \exp(j*(2\pi))^{0.5} = 1^{0.5} = 1$$
Well $1$ is not equal to $-1$. What did i do wrong?
Thank you