Reactivating license after OS re-installation

I am using Unity Android+iOS license, which I got in the free offering going on a few months back.

Now I am to re-install my operating system (Windows 7).

How I am going to backup my license, so that I can reactivate it later?

The license terms specifically allow you install on up to two machines concurrently, as long as you don’t use them at the same time – you should be able to activate the new install with the same serial key you’ve been using.

You could also get in touch with Unity Technologies support, directly; they probably have an established and authoritative answer for this question. It’s mentioned on this FAQ page, for example.