So I've got this question that is a bit difficult to ask, since it uses a term in my language that I can't properly translate into English.
For $z\in\mathbb{C}^*$ and $a\in\mathbb{C}$ it would be natural to define $z^a=exp(a\cdot log(z))$, with $log(z)$ being a complex number so that $exp(log(z))=z$. I have a problem however, since $log(z)$ isn't single-valued. I'm asked to give combinations of $a$ and $z$ for which the definition is single-valued.