I am not certain from your description what you want to plot.
Try this:
ang = 0:0.1:2*pi;
z = exp(1i*ang);
f = @(z) 1./z;
figure
plot(real(f(z)), imag(f(z)))
axis equal
figure
plot(ang, real(z))
hold on
plot(ang, imag(z))
hold off
grid
The first figure plots the imaginary component as a function of the real component. The second plots both as a function of ‘ang’.
