Question

Let $\omega$ is the root of the equation $x^2+x+1=0$ whose imiginary part is postive and $|z-\omega |=|z+\omega |$, then $\arg \left(z\right)$ is

• A. $\frac{\pi }{3}$
• B. $\frac{5\pi }{6}$
• C. $\frac{\pi }{6}$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is C $\frac{\pi }{6}$

Locus of $z$ is the perpendicular bisector of the line segment joining $\omega$ and $-\omega$
$\therefore \arg \left(z\right)=\frac{\pi }{6}$