I'm starting just starting complex number geometry and I'm having trouble with understanding the basic theorems
if A, B, C, D are pairwise distinct points then
$\frac{d-c}{b-a} $ is purely imaginary, then AB is perpendicular to BC
I don't know how to prove this since I don't know what $d-c$ and $b-a$ represents in the graph
Assuming $a$ is the complex number represented geometrically by the vector $OA$, where $O$ is the origin, and similarly for $b, c, d$, then the difference $b-a$ is represented by the vector $AB$, and $d-c$ by $CD$.
For concluding the exercise, note that multiplying a vector by $i$ is just rotation by $+90^\circ$.