HOW CAN I SYNC MY IPHONE TO MY NEW COMPUTER WITHOUT LOSING ALL THE APPLICATIONS THAT I’VE BOUGHT?

I do not caring if it stays synced to my old PC, all I wish is to sync it to my brand brand new one and not lose any of my applications. Does iTunes store all of my purchases? Once it erases the iphone to sync to a brand brand new one will iTunes collect my lost applications? Any help?