Let a circle $C$ in complex plane pass through the points $z _ { 1 } = 3 + 4 i , z _ { 2 } = 4 + 3 i$ and $z _ { 3 } = 5 i$. If $z \neq z _ { 1 }$ 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\\
(1) $\tan ^ { - 1 } \frac { 24 } { 7 } - \pi$\\
(2) $\tan ^ { - 1 } \frac { 2 } { \sqrt { 5 } } - \pi$\\
(3) $\tan ^ { - 1 } 3 - \pi$\\
(4) $\tan ^ { - 1 } \frac { 3 } { 4 } - \pi$