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(≠ z_1) is a point on C such that the line through z…

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