# The locus of z satisfying arg

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