Let $$f(z)=\gamma + z^{\beta_2-\beta_1}$$ where $\gamma\in \mathbb{R}$, $\beta_1\in \mathbb{Z}$, $\beta_2 \in \mathbb{Z}$ and $\beta_2 > \beta_1$. The variable $z$ takes complex values.
Is there a way of expressing the zeros of $f(z)$ in terms of the parameters ($\gamma,\beta_1,\beta_2$)?