Let $S$ be the set of all complex numbers $z$ satisfying $| z - 2 + i | \geq \sqrt { 5 }$. If the complex number $z _ { 0 }$ is such that $\frac { 1 } { \left| z _ { 0 } - 1 \right| }$ is the maximum of the set $\left\{ \frac { 1 } { | z - 1 | } : z \in S \right\}$, then the principal argument of $\frac { 4 - z _ { 0 } - \overline { z _ { 0 } } } { z _ { 0 } - \overline { z _ { 0 } } + 2 i }$ is (A) $- \frac { \pi } { 2 }$ (B) $\frac { \pi } { 4 }$ (C) $\frac { \pi } { 2 }$ (D) $\frac { 3 \pi } { 4 }$
Let $S$ be the set of all complex numbers $z$ satisfying $| z - 2 + i | \geq \sqrt { 5 }$. If the complex number $z _ { 0 }$ is such that $\frac { 1 } { \left| z _ { 0 } - 1 \right| }$ is the maximum of the set $\left\{ \frac { 1 } { | z - 1 | } : z \in S \right\}$, then the principal argument of $\frac { 4 - z _ { 0 } - \overline { z _ { 0 } } } { z _ { 0 } - \overline { z _ { 0 } } + 2 i }$ is\\
(A) $- \frac { \pi } { 2 }$\\
(B) $\frac { \pi } { 4 }$\\
(C) $\frac { \pi } { 2 }$\\
(D) $\frac { 3 \pi } { 4 }$