1. The problem statement, all variables and given/known data Solve the following equation: [tex]z^4+z^3+z^2+z+1 = 0[/tex] z is a complex number. 2. The attempt at a solution I was trying to factorize it to 1st degree polynomial multiplied by 3rd degree polynomial: [tex](z+a)(z^3+bz^2+cz+1/a) = 0[/tex] I discovered that I need to solve 3rd degree polynomial just to do that. [tex]a^3-a^2+1 = 0[/tex] This is too much mess for a small homework exercise. I think that there is a technique that I am not aware of. Thank You.