Broken banana plug and stuck in amplifier

Any chance you can insert a drill bit that is smaller than the piece you are trying to remove? Wedge it in there and spray a small amount of WD40 to reduce any friction, then using pliers turn the bit to a point of engaging the banana piece the pull on the drill bit. If any movement is witnessed then repeat the process except the WD40 and it should work out a little at a time. 
if you use the rat tail file make sure to insert the tang in as the file is designed to cut on the push stroke and won’t engage the broken piece as you pull.

good luck

There are small special wire locksmith use to pull out broken keys in locks. Can probably find them on Amazon. They have one way teeth to grab the stick piece. 

That just happen to me! I used a drill ( very carefully)with the correct size drill bit and Bob your uncle

Many thanks for all your suggestions and safety precaution.

I managed to use tweezer to slowly and hold tight on the tip of tweezer to pull out gently without damaging the terminal (the broken banana plug tip was split in loose, so use tweezer to grab the short piece and pull.  (The tweezer is with anti-static tip, used to pick screw from PCBs) 

From the bad experience of banana plugs, I would use spades type speaker cable instead next time.

Your 400 (and above) series Dyson should have included a BBPE (Broken Banana Plug Extractor) tool.  Just connect the accessory, hit the power button and suck it right out.