Lorentz poles in complex plane

Function lorentz_poles(n) generates poles ( or peaks) in the complex plane z=x+iy, using the nth version of Lorentz function (1+z^n)^(-1). The poles are located in the perimeter of the unit circle. The function is slightly altered by a multiplication of sin(z) and can be adjusted for simulating any related Physics phenomena.
If the input n is real then the function generates p=floor{n} poles if p is even, or p+1 poles if p is odd.
demo1 : To produce the snapshot.
% figure(1);
% set(figure(1),'Position',[237 117 941 549]);
% for n=1:8
% subplot(2,4,n)
% lorentz_poles(n);
% end