Question:
The locus of $z$ satisfying $\arg (z)=\frac{\pi}{3}$ is _______________
Solution:
Given arg $(z)=\frac{\pi}{3}$ and for $z=x+i y$
$\frac{\pi}{3}=\tan ^{-1}\left(\frac{y}{x}\right)$
i. e $\tan \frac{\pi}{3}=\frac{y}{x}$
i. e $\sqrt{3}=\frac{y}{x}$
i.e $y=\sqrt{3} x$ in I quadrant except origin