<s>[INST] 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?
 [/INST] Just multiply the fraction by the complex conjugate of $z+1$, that is,
\begin{equation*}
\frac{z}{z+1} = \frac{x+iy}{1+x+iy} = \frac{1+x-iy}{1+x-iy} \frac{x+iy}{1+x+iy} = \frac{(1+x)x+y^2+iy }{(1+x)^2+y^2} =
\end{equation*}
\begin{equation*}
= \frac{(1+x)x+y^2}{(1+x)^2+y^2} + i \frac{y}{(1+x)^2+y^2}
\end{equation*}
</s>