Find the real and imaginary part of the following I'm having trouble finding the real and imaginary part of $z/(z+1)$ given that z=x+iy.  I tried substituting that in but its seems to get really complicated and I'm not so sure how to reduce it down.  Can anyone give me some advice?

$$\begin{align}
&\frac{z}{z+1}\\
=& \frac{x+iy}{x+iy+1}\\
=&\frac{x+iy}{x+iy+1}\times \frac{x-iy+1}{x-iy+1}
\end{align}$$
I'm sure you can take the rest from here.
