AIME Class: Complex Numbers and Polynomials

Today I had a meeting of my AIME class. The topics being discussed were complex numbers and polynomials, and though neither o these topics is my strong point, the class wasn't that bad.

Here's an interesting problem (interesting because although it looks like a simple arithmetic problem, in reality the solution involves polynomials):



(Note that calculators are not allowed on the AIME.)

I'll let this one stand for a few days, then I'll post the answer. Try doing this without a calculator! :p