On two classes of dense 2-generator subgroups in $\mathbb{C}$

Abstract

We consider dense 2-generator multiplicative subgroups in $\mathbb{C}$ and show that for each point $z\in \mathbb{C}$ the set of limit values for the arguments of the powers of each generator at the point $z$ is either finite or is $[-\pi ,\pi ]$

7 pages