Yeah, ehroof you are correct ... here is what Futaba FAQ's say:

"Part of my FM receiver antenna ripped off. Can I solder a new piece onto it?
While we can not recommend that anyone change their receiver wire, as this can cause serious problems such as loss of reception and major interference issues, and also void any warranty that you may have on your radio system.

If you are very good with a soldering iron, and safety consideration (do a COMPLETE and thorough ground check, after for safety purposes) and the warranty are not a issue, you would want to look for 22 gauge wire, and the length will be:

approximately 19 1/2" for surface
approximately 39 1/2" for Air

BUT, our recommendation is to send the receiver into our Service Center to be repaired."