If $\omega$ is the $n$th root of unity then

Question

$$\begin{array}{1 1}(1)1+\omega^{2}+\omega^{4}+\dots=\omega+\omega^{3}+\omega^{5}+\dots&(2)\omega^{n}=0\\(3)\omega^{n}=1&(4)\omega=\omega^{n-1}\end{array}$$