"Teil 1\n\nNullstellen: ´x^6 = -1 = e^(i pi)´\n\n´x^6 = e^(i pi) = e^(i (pi + k \* 2pi))´ ´k in ZZ´\n\n´=> x_k = e^(i((pi + k \* 2pi)/6))´\n\n´k: 0,1,…,6´\n´=> x^6+1 = (x - e^(i pi/6)) \* ´´(x - e^(i (3pi)/6)) \* ´´(x - e^(i (5pi)/6)) \* ´´(x - e^(i (7pi)/6)) \* ´´(x - e^(i (9pi)/6)) \* ´´(x - e^(i (11pi)/6))´\n\nUmwandlung in arithmetische Form fehlt!\n\n\nTeil 2\n\n´(x - e^(i pi/6))(x - e^(i (11pi)/6))´\n´= x^2 - (e^(i pi/6) + e^(i (11pi)/6)) + e^(i pi (1/6 + 11/6))´\n´= x^2 - Re(e^(i pi/6))x + 1´\n\n\n´x^6 + 1 = (x^2 - cos(20˚)x + 1) \* ´´(x^2 - cos(40˚)x + 1) \* ´´(x^2 - cos(60˚)x + 1) \* ´´(x^2 - cos(80˚)x + 1) \* ´´(x^2 - cos(100˚)x + 1) \* ´´(x^2 - cos(120˚)x + 1)´\n\n\nTeil 3\n\n´-1 = 1´ in ´ZZ_2´\n\n´x^6 + 1 = x^6 - 1´\n´= (x^3)^2 - 1^2´\n´= (x^3 + 1)(x^3 - 1)´\n´= (x^3 - 1)^2´\n´= (x^3 - 1)^2´\n\nEnde fehlt\n\nFür ´x^8 + 1´:\n\n´x^8 + 1 = x^8 - 1´\n´= (x^4)^2 - 1^2´\n´= (x^4 + 1)(x^4 - 1)´\n´= (x^4 - 1)^2´\n´= ((x^2)^2 - 1^2)^2´\n´= ((x^2 + 1)(x^2 - 1))^2´\n´= ((x^2 - 1)^2)^2´\n´= (x^2 - 1)^4´\n´= ((x - 1)(x + 1))^4´\n´= (x + 1)^8´"