# If w is a complex cube roots of unity then w^17: 1. 0 2. 1 3. w 4. w^2 Pleas explain?

$\omega \in \mathbb{C}$ is a cube-root of unity $\therefore {\omega}^{3} = 1.$
$\therefore {\omega}^{17} = {\omega}^{15 + 2} = {\omega}^{15} \cdot {\omega}^{2} = \left({\left({\omega}^{3}\right)}^{5}\right) \cdot {\omega}^{2} = \left({\left(1\right)}^{5}\right) \cdot {\omega}^{2} = {\omega}^{2.}$
$\therefore \text{ Answer : Option 4. } {\omega}^{2.}$