Exercise 6.10 Frequency dependencies in a unity gain configuration

In the voltage follower below, the opamp is not ideal. It does have a very high input impedance $r_{\mathit{in}}$, its open loop voltage gain is $A(\mathit{j\omega })=\frac{A_0}{1+\mathit{j\omega }{\tau }_1}$, and its open-loop output resistance $r_{\mathit{out}}$ is non-zero.

a)

Derive an expression for the output impedance $r_{\mathit{out},\mathit{circuit}}$ of the circuit above, looking into $v_o$. Manipulate it to standard form and draw a bode plot (magnitude and phase). Indicate the values of poles, zeros (x-axis) and flat parts (y-axis).