Complex function : composition of a translation, rotation, etc

I don't know how to approach the following problem : Write the transformation $\displaystyle T(z)=\frac{i-z}{i+z}$ as a composition of translations, rotations, dilatations and inversions. Use the result to find the image of the semi-plane $\displaystyle y>0$.

My attempt : My idea was to write $\displaystyle T(z)$ in the form $\displaystyle re^{i \pi \theta}$ but I didn't reach anything important I believe.

So I guess there's a better way to approach the problem. I'd like to know it/them.