These two are giving me a bit of trouble...

I think I'm missing the point on this one, I know I could right everything out in terms of sin and cos, but there's got to be an easier and quicker way...

43. If z=exp(2*pi*i/5), then find 1 + z + z^2 + z^3 + 5z^4 + 4z^5 + 4z^6 + 4z^7 + 4z^8 + 5z^9.

I'm not even sure how to approach this one...

49. Up to isomorphism, how many additive abelian groups G of order 16 have the property that x + x + x + x = 0 for each x in G?

Peter