Real and Complex number systems

Hi there... I'm back in school after ten years, and I must say my math is a little rusty. I could use some help-with some explanation....so I can truly follow and understand.

I am given this:

x=r(cos u + i sin u) and y=t(cos v + i sin v)

and I'm being asked to (1) prove that the modulus of (xy) is the product of their moduli, and (2) prove that the amplitude of (xy) is the sum of their amplitudes, showing each step of both proofs.

I understand modulus with respect to the time of day using a 12 hour clock, but I'm finding it hard to apply, nevermind prove this situation. Just need some direction!!!! Thanks so much.