I understand the current calculation. What I dont understand is why the 5 kOhm resistors voltage drop does not need to be taken into account when finding v2. The book says v2 is the same as the voltage across the 4 kOhm resistor. Why do you not need to take into account the voltage drop across the 5 kOhm resistor?
Under DC conditions, the capacitor will be as fully charged as it will ever be.
That implies that the current through the capacitor has dropped to zero, so the current through the 5K resistor is also zero. So the voltage across the resistor is zero.