Question

If a complex number $\omega$ satisfies the equation ${\omega }^3=1$ then value of $1+\omega +\frac{1}{\omega }$ is

• A. $0$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is A $0$

Given $w^3=1$ (or) $\omega =(1{)}^{1/3}\Rightarrow \omega$ is the cube root of unity.
So, $1+\omega +\frac{1}{\omega }=1+\omega +{\omega }^2=0$ $[\because \frac{1}{\omega }=\overline{\omega }={\omega }^2]$