Suppose I have an arbitrary triangle, $ADC$, oriented in a clockwise fashion. Using complex numbers $a$, $d$ and $c$, we represent the vertices $A$, $D$ and $C$ respectively.
My question is: If I would like to find the angle $ADC$ in terms of $\arg(.)$ and $a$, $d$ and $c$, how can I write them?
My guess is: $\angle ADC=\arg(d-c)-\arg (d-a)=\arg \bigg(\dfrac{d-c}{d-a} \bigg)$.
If I am wrong, what should it be then? Also, can someone kindly help me to understand the problem geometrically? My apologies if the question is trivial but I am having a really hard time trying to visualise how to set up the problem. Thank you in advance.
Yes it is right, we are using the basic properties of complex numbers. Just recall to assume $\arg$ defined in a proper interval as $[0,2\pi)$.
In order to visualize better let consider $D$ as the origin then we obtain
$$\angle ADC=\arg(c’)-\arg(a’)=\arg(c’/a’)=\arg \bigg(\dfrac{c-d}{a-d} \bigg)$$