Sketching Frequency domain repsonses

[ineedmunchies]

Homework Statement

Sketch the z-plane pole zero diagram for:
$$G(z) = \frac{z^{2} + z + 1}{z^{3}}$$

Also sketch the time and frequency domain repsonses, the latter in amplitude and phase.

Homework Equations

$$G(z) = \frac{Y(z)}{X(z)}$$

Zeros when $$Y(z) = 0$$;

Poles when $$X(z) = 0$$

For frequency reponse:
$$|G(\omega)| = \frac{\prod Distance from Zeros}{\prod Distance From Poles}$$

$$\angle G(\omega) = \sum Angles from Zeros - \sum Angles from Poles$$

The Attempt at a Solution

I have found that there is a pole at zero and two zeros at -0.5 on the real axis.

However I cannot figure out how to calculate or even sketch from inspection the magnitude and phase frequency response.

I have looked at a few different sources and have got somewhat confused at to what point this calculation should be made. Say for example I wanted to figure out the magnitude response at $$\omega = 0$$, $$\pi$$ and $$2\pi$$. Would I calculate these distances to a point on the unit circle that corresponds to this value of $$\omega$$ or to a point on the real axis, or another point altogether.

I'm confused! Any help at all would be appreciated!

 

[ineedmunchies]

Ok so I figured this out straight away after posting. I meant to say that I found two zeros at -1. I then realized that I need to calculate for points around the unit circle, starting from 1 on the real axis and moving anti clockwise around the unit circle. Thanks for anyone that took time to read this.