Don't understand this zero pole plot example
For readers who would like to determine the transfer function of this filter but also for the sake of a simple personal exercise, I have applied the fast analytical circuit techniques or FACTs described in my last book. The principle is simple and consists of determining the time constants of this 2nd-order circuit in two conditions: when the excitation is zeroed (the input source is replaced by a short circuit) and when the output is a null (no ac response) despite the excitation being back in place.
We start with \$s=0\$ and open-circuit all capacitors, exactly as SPICE does when determining a dc operating point. When you do this, the circuit becomes a simple resistive divider and if all resistors are equal, the gain is 0.5 or -6 dB. Then you carry as shown in the below drawings:

What is cool is that you determine all time constants by inspection without the need to resort to algebra: less mistakes and you can easily come back to a faulty sketch and fix it individually leaving the rest intact. If all goes well, you have the following expressions:

I have derived the expression with different values for the resistors and capacitors but if you consider all resistances equal to \$R\$ and the capacitors equal to \$C\$, then you can simplify the expression and factor the denominator as the product of two separated poles after solving a simple two-unknown equation and confirm the coefficients given in the text:

We can now plot and compare the reference response given by the brute-force approach and that of the FACTs. As you can see, they are rigorously identical: