Consider the following four propositions
$P _ { 1 }$: If complex number $z$ satisfies $\frac { 1 } { z } \in \mathbf { R }$, then $z \in \mathbf { R }$;
$p _ { 2 }$: If complex number $z$ satisfies $z ^ { 2 } \in \mathbf { R }$, then $z \in \mathbf { R }$;
$p _ { 3 }$: If complex numbers $z _ { 1 }$, $z _ { 2 }$ satisfy $z _ { 1 } z _ { 2 } \in \mathbf { R }$, then $z _ { 1 } = \overline { z _ { 2 } }$;
$p _ { 4 }$: If $z + \bar { z } \in \mathbf { R }$, then $z \in \mathbf { R }$.
The true propositions are
A. $p _ { 1 } , p _ { 3 }$
B. $p _ { 1 } , p _ { 4 }$
C. $p _ { 2 } , p _ { 3 }$
D. $p _ { 2 } , p _ { 4 }$