what is the frequency response? I try to work out the simplest system, whose response is $H(z) = 1 + cz + c^2z^2 + c^3z^3 + \cdots = 1 / (1-cz)$ 

Now, Z-transform done quick (Fourier connection) and 4.5 Transfer Function, Poles and Zeros say that we just need to plug $z =&gt; e^{iw}$ to get the frequency response. I am getting single pole at $w = i \ln c$. It is complex. What is the frequency response? The second link says that real coefficients must generate complex poles in pairs. Where is the second pair?
Frequency response is $1/(1−ce^{iw})$, if you want to get amplitude information you just need to get the magnitude of this complex function and its phase will be the inverse of the phase of $1/(1−ce^{iw})$ or 

$$-\arctan (-c\sin w/(1-c\cos w))$$

You can compute the magnitude of the transfer function by:

$$ 1 / sqrt( (-c\sin w)^2 + (1-c\cos w)^2 )$$