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?
[Math] Find the real and imaginary part of the following
complex numberscomplex-analysis
Best Answer
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*}