# graph of poles at the same location

Just wanted to make sure:

This cases would have three poles at the exact same location of (z=1) on the complex plane?

$$H(z)=\frac{1}{(z-1)^3}$$

But this case, would have three poles spread out on a circle of complex plane:

$$H(z)=\frac{1}{z^3-1}$$

$$H(z)=\frac{1}{\left(z-1\right)\left(z-0.5-i\sqrt3/2\right)\left(z-0.5+i\sqrt3/2\right)}$$

Exactly. In the first case you have all 3 poles $$z_{1,2,3}=1$$ in a real part of the complex plane.
$$z_1 = 1$$ , $$z_2 = - \frac{1}{2} + \frac{1}{2}\cdot\sqrt{3}i$$, $$z_3 = - \frac{1}{2} - \frac{1}{2}\cdot\sqrt{3}i$$