Pregunta: 14. Determine all Möbius transformations M of the upper half-plane mapping the line C(−1,1)= {eit∣0

14. Determine all Möbius transformations $M$ of the upper half-plane mapping the line $C(-1,1)=$ $\left\{e^{it}\mid 0<t<\pi \right\}$ to $C(0)=i{\mathbb{R}}^{+}$, i.e, so that $\forall t\in (0,\pi )\exists \lambda \in {\mathbb{R}}^{+}:M(i\lambda )=e^{it}.$ Hint: Look at ideal points. Problem 18 might help.