Question

${\omega }^{29}+{\omega }^{28}+1=?$, where $\omega$ is a cube root of unity.

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $0$

Given, ${\omega }^{29}+{\omega }^{28}+1$
$=({\omega }^3{)}^9{\omega }^2+({\omega }^3{)}^9\omega +1$
$={\omega }^2+\omega +1$ [$\because {\omega }^3=1$]
$=0$ [$\because$ sum of cube roots of unity is equal to zero]
Option $A$ is correct.