Let a circle C in complex plane pass although the points $z_1=3+4 i, z_2=4+3 i$ and $z_3=5 i$. If $z\left(\neq z_1\right)$ is a point on C such that the line through $z$ and $z_1$ is perpendicular to the line through $z_2$ and $z_3$, then $\arg (z)$ is equal to :
