Electrical – Does a voltage source produce current on an open branch

That could only be replaced by an infinite voltage source.

Current sources operate on the basis that they will output their current no matter the load. When you leave it open circuit your open circuit voltage would be infinity. IE, this circuit cannot exist.

The standard replacement will be a current source with a parallel resistance to a voltage source with series resistance. As shown in this wikipedia image.

http://en.wikipedia.org/wiki/Th%C3%A9venin's_theorem">

The Thevenin voltage looking into the terminals A & B can be found by inspection using superposition.

\$V_{th} = (-j2A) \cdot (-j4\Omega) + j4V \$

The first term is found by zeroing the voltage source on the right and the second term is found by zeroing the current source on the left.

The Thevenin impedance is easy too; simply zero both sources to get:

\$ Z_{th} = -j4 \Omega\$

The current is then found to be:

\$I_{resistor} = \dfrac{V_{th}}{Z_{th} + 8 \Omega}\$

I highly recommend reviewing the late Dr. Leach's notes on using superposition. I've taught it this way for years. If you practice using superposition, you will amaze your friends and professors alike by solving many circuits by inspection.