[tex]\it z^3=1 \Rightarrow z^3-1=0 \Rightarrow (z-1)(z^2+z+1)=0 \Rightarrow z_1=1,\ \ z_{2,3}=-\dfrac{1}{2}\pm\dfrac{\sqrt3}{2}i\\ \\ \\ \alpha\ne1 \Rightarrow \alpha=-\dfrac{1}{2}\pm\dfrac{\sqrt3}{2}i\\ \\ \\ |\alpha|=\sqrt{\dfrac{1}{4}+\dfrac{3}{4}}=\sqrt{1}=1[/tex]
