Let $z=x+iy$, $w=a+ib$. Show that the angle of line $WZ$ makes with the positive real axis is $\arg (z-w)$

Question

I'm struggling to understand why the line $WZ$ is can be represented as $z-w$.

Can someone point me in the right direction??

Answer 1

Notthe line, but the vector. That's simply because the image of $w$ in the Argand-Cauchy plane, with origin $O$ is vector $\overrightarrow{OW}$, the image of $z$ is vector $\overrightarrow{OZ}$ and $z-w$ has image $$\overrightarrow{OZ}-\overrightarrow{OW}=\overrightarrow{ZW}.$$

Answer 2

The vector $z-w $is the same as the vector $WZ $so they have the same argument.