The Sims 3 has a limited number of computers where it can be installed at any time. By de-authorizing a machine you are allowing one of those limited spots to be freed up and therefore should be able to install the game on a new computer without further issues.
To use the in-game de-authorization tool for The Sims 3, follow the steps below:
De-authorization applies only to digitally downloaded copies of The Sims 3. The retail disk version of The Sims 3 requires the disk in the drive to launch and play the game, and does not use DRM with machine limitations.
You should get a message alerting you de-authorization was successful once the Launcher is finished de-authorizing your machine. Keep in mind de-authorization does not uninstall the game. If you decide you want to re-authorize your computer later, all you have to do is re-launch the game.