gain of inverting op amp with resistor on input
Your conclusion that Vout = - Vin is correct.

Capacitor C and resistor R2 are just there to confuse you. As there is no current flowing into (or out of) the + input of the opamp, Vin+ = 0

The opamp will try to make Vin- = 0 as well if possible. Let's assume the opamp can manage that so we assume Vin- = 0

That means the current Iin = Vin / Rin with In flowing in the direction as shown. This Iin cannot flow into the opamp's - input, all of it has to go through the other resistor R1. The left side of R1 will be at 0 V, the current will flow from left to right and that means that Vout has to be negative with a value of Vout = Iin * R1.

So Vout = - Vin.