For a non-zero complex number $z$, let $\arg ( z )$ denote the principal argument with $- \pi < \arg ( z ) \leq \pi$. Then, which of the following statement(s) is (are) FALSE?
(A) $\arg ( - 1 - i ) = \frac { \pi } { 4 }$, where $i = \sqrt { - 1 }$
(B) The function $f : \mathbb { R } \rightarrow ( - \pi , \pi ]$, defined by $f ( t ) = \arg ( - 1 + i t )$ for all $t \in \mathbb { R }$, is continuous at all points of $\mathbb { R }$, where $i = \sqrt { - 1 }$
(C) For any two non-zero complex numbers $z _ { 1 }$ and $z _ { 2 }$, $$\arg \left( \frac { z _ { 1 } } { z _ { 2 } } \right) - \arg \left( z _ { 1 } \right) + \arg \left( z _ { 2 } \right)$$ is an integer multiple of $2 \pi$
(D) For any three given distinct complex numbers $z _ { 1 } , z _ { 2 }$ and $z _ { 3 }$, the locus of the point $z$ satisfying the condition $$\arg \left( \frac { \left( z - z _ { 1 } \right) \left( z _ { 2 } - z _ { 3 } \right) } { \left( z - z _ { 3 } \right) \left( z _ { 2 } - z _ { 1 } \right) } \right) = \pi$$ lies on a straight line