We have a complex number ω = cos(2π/5) +isin(2π/5) and we have two complex numbers a and b, such that: a= ω + ω4 and b= ω2 + ω3. I have to prove that a + b = -1 and a*b= -1. Then, based on that, determine cos(2π/5) and sin(2π/5). I've tried to solve this using trigonometry. First a+b, i got: cos(2Pi/5) + cos(4Pi/5) + cos(6Pi/5) + cos(8Pi/5) + i[ sin(2Pi/5) + sin(4Pi/5) + sin(6Pi/5) + sin(8Pi/5)] then i tried expressing cos(6Pi/5) as cos(2Pi/5 + 5Pi/5) = cos(2Pi/5)cos(4Pi/5) + sin(2Pi/5)sin(4Pi/5) and cos(4Pi/5) as cos2(2Pi/5) - sin2(2Pi/5). But that wasn't helpful. Knowing that a + b equals -1 that means that this whole expression should end up as cosPi + isinPi since that is equal to -1. But i just can't get there.