I say it is not a proof. When you get to saying "z = 10 roots of unity" and "z = 8 roots of -1" those are contradictory statements. There are no roots that satisfy both conditions. However we know there are 10 roots over C for the original equation.
I went and plugged the original equation into wolframalpha, and the plot of solutions looks like 10 of the 20 roots of -1.
re: Possible proof
