Question

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

The function ƒ : $\to$ (–$\pi ,\pi$], defined by ƒ(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 z₁ and z₂ $\left(\frac{Z_1}{Z_2}\right)$ -arg$\left(Z_1\right)$+ arg z(Z₂)arg  is an integer  multiple of $2\pi$

For any three given distinct complex numbers z₁, z₂ and z₃, 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