Let $M$ be a Moebius transformation of the hyperbolic upper halfplane so that $M$ maps the imaginary axis $i\mathbb{R}^+ = \{it \mid t \in \mathbb{R}^+\}$ to the hyperbolic line \begin{align*} C(1,3) = \{2 + e^{it} \mid 0 < t < \pi\} \end{align*} and so that $M(i) = 2 + i \in C(1, 3)$. Determine the hyperbolic line $M(C(-1, 1))$, for instance in terms of ideal points.