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 ?
Select ALL correct options:
A
$\arg (-1-i)=\frac{\pi}{4}$, where $i=\sqrt{-1}$
B
The function $f: R \rightarrow(-\pi, \pi]$, defined by $f(t)=\arg (-1+i t)$ for all $t \in R$, is continuous at all points of $R$, 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 $\mathrm{z}_1, \mathrm{z}_2$ and $\mathrm{z}_3$, 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
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