Yes! In fact, you can rotate i (or 1) by any angle around the origin and obtain a so-called "root of unity". If the angle was rational, you can now apply this r

Yes! In fact, you can rotate i (or 1) by any angle around the origin and obtain a so-called "root of unity". If the angle was rational, you can now apply this rotation multiple times to itself and eventually you'll obtain 1 or -1.