I have the following function:
B[z_]=((z*(z - 0.5)*(z + 0.5))/((1 - 0.5*z)*(1+0.5*z)))
I want to plot the roots this polynomial according to angel like below the picture with Mathematica.
I post this exploration just for fun. Setup:
The mesh is the unit circle, the red points are the roots of the rational function.
A "prettier" version:
Showing the zeroes and poles in 3D (using Abs[B[z]-1]):
How about this:
update: to add line between each point:
For many more roots, to display by angle order:
Is this what you mean?
Since the OP's graphic appears to also show the poles I would add those
For more complicated cases to avoid crossing lines use ListCurvePathPlot (new in v7)
Mathematica loves to work with complex numbers--except when it comes to graphing! Adopting the principle that what starts as complex should stay as complex, we may directly graph the complex roots without splitting each into its real and imaginary parts. To do that, we employ David Park's Presentations add-on (http://home.comcast.net/~djmpark/DrawGraphicsPage.html).
For a somewhat fancier graphic that includes tooltips showing the exact values of the roots, begin by rationalizing the given function and computing the roots exactly: