Find Thevenin resistance

Today, I get stuck in finding Thevenin resistance for the circuit in attached file.
The circuit has I0=2A, Z= 2Ω, R1=2Ω, R2 =4Ω.
To calculate Thevenin resistance, I connnected port A with 4V voltage source.
I2 = 4V/R2= 4V/4Ω = 1A
Apply KVL for the closed path R1, R2, Zi:
4 = Z*i + R1*i= 2i + 2i =4i
=> i = 1A
Apply KCL at A:
I1 = I0 - i = 2A- 1A=1A
Apply KCL at B:
I3 = I2 - I1 = 1A -1A =0
=> Rth = 4V/ I3 = 4/0 = ∞ ???
I don't know where I am wrong here? Please help.

 

You answer looks good, But what you found is not a Rth. To find Rth you need to replace Io current source with a open circuit.

 

Oh, thanks Jony! I see it. I don't know why I forgot it!
Yes, with current source open, I can easily find Rth = 2Ω now.

 

I've got the same answer as you.