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?

$$arg(-1-i)=$$\frac{\pi}{4}$$,where i=\sqrt{-1}$$

The function f:R $$\rightarrow (-\pi, \pi]$$, defined by f(t)= arg(−1 + it) for all t $$\in$$ R, is continuous at all points of R, where $$i=\sqrt{-1}$$

For any two non-zero complex numbers $$Z_{1} and Z_{2}$$, $$arg(\frac{Z_{1}}{Z_{2}})-arg(Z_{1})+arg_{Z_{2}}$$ is an integral multiple of $$2 \pi$$

For any three given distinct complex numbers $$Z_{1}, Z_{2}$$ and $$Z_{3}$$ the locus of the point Z satisfying the condition arg $$\left(\frac{(Z-Z_{1})(Z_{2}-Z_{3})}{(Z-Z_{3})(Z_{2}-Z_{1})}\right)=\pi$$ lies on a straight line