If you can see the broken end inside the jack you could try this method. Straighten out a paper clip, dip the end in Superglue and place on end of broken piece, WAIT, then gently twist and pull. May take a couple of attempts, good luck.
"Tried everything i can to get it out but it wont budge."
Get a short length of copper wire (The conductor wire from 2.5 Twin and earth power cable is perfect) and some Araldite two-part adhesive. Mix up some adhesive and put a tiny blob on the end of the copper wire.
Insert the end of the wire until the adhesive touches the broken headphone jack. Now comes the hard part - you have to find a way to keep the wire in place while the adhesive cures overnight. A small roll of paper works well as a wedge. The important thing is not to let the adhesive come into contact with the sides of the hole - use only a very small amount.
If you get it right, you will be able to pull gently on the wire in the morning, and withdraw the broken part.
Proceed at your own risk. The worst thing that can happen is that you glue the broken part to the inside of the hole.