Suppose $T$ is a linear fractional transformation such that $T(0)=1, T(1)=i,$ and $T(\infty)=0$. Find $T(i)$ and describe $T(R)$, where R is the real line.
I ended up getting $T(z)=\frac{1}{(-i-1)z+1}$, and I am pretty sure this is correct. I am lost on what $T(Z)$ does to the real line.