No, you don't need to re-purchase them. I forget the exact solution, but I think it's to go into Settings->Apps, find Google Play Store and clear the cache. Generally I do the same for Google Play Services and Google Services Framework. It's cache you are clearing, not data.
If, after a reboot you still don't see the apps as purchased you might then resort to clearing the data. Doing so would have the side-effect of having to login again when you start the Play Store.
Others might be able to give a more exact answer. It's been awhile since I had the problem.
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