I want to find $z,w,\lambda \in \mathbb{C}$ such that $(zw)^{\lambda}\neq z^{\lambda}w^{\lambda}$. I wasn't able to find an example so far.
If you take $z$ and $z^{-1}$, then $(zw)^{\lambda}=z^{\lambda}w^{\lambda}$. If $z=1+i, w=-1+1$ and $\lambda =i$ it works out too.
The authors are defining $z^{\lambda}$ as $e^{\lambda \operatorname{Log}(z)}$.
I would appreciate any hint!