1. The problem statement, all variables and given/known data
Find the input impedance.

2. Relevant equations

3. The attempt at a solution
Input impedance= R1. I don't get why we can ignore the other resistors.

Problem 2 :

1. The problem statement, all variables and given/known data
Find the gain of the system.
https://www.physicsforums.com/attachment.php?attachmentid=68909&stc=1&d=1398116979 2. Relevant equations

3. The attempt at a solution
Gain = 2

My professor wrote
vout= (R3/R2) Vin + vin = 2Vin, so gain =2.
I understand that (R3/R2) Vin is from the output of the op amp but I do not know where the other Vin came from.
Can someone explain this please?

Use the known behavior of an ideal op-amp (regarding input impedance at its inputs and the voltage between its input terminals when there's feedback) to say something about the currents though R3 and R4. What will be the voltage at input terminals of the op-amp?

Note that I'm presuming that the pin layout for the op-amp is the same as the standard 741 op-amp. It would be preferable to label the inputs as + and - on your diagrams instead of just putting pin numbers.

Hmm. That doesn't look like the gain of the given circuit to me. Surely R4 and R1 should be involved in setting the gain?

The current into 2 and 3 is zero using the golden rule. The voltage at 2 and 3 does not necessarily have to be Vin right, since current can flow to R4. So would you have to call it something else?

The voltage difference is 0. Say I call the voltage at the inputs v2. So the input current is (V2- Vin)/R1?
Zin= Vin / ((V2- Vin)/R1) But this doesn't seem right...

The current through R2 would be zero. Therefore V2=0 since there is no current into input 3. Iin would be Vin/ R1 so the input impedance is Vin / (Vin/ R1) = R1?

Thank you so much, gain = -R4/ R1! And if possible could you help me out with my second question? We are asked the voltage gain of the system, vout/vin.