I have a relatively simple question but I am scratching my head to come up with a solution that satisfies me.
In the Argand diagram, ABCD is a square, and OE and OF are parallel and equal in length to AB and AD respectively. The vertices A and B correspond to the complex numbers $w_1$ and $w_2$ respectively. What complex numbers correspond to the points E, F, C and D?
So $AB$ = $w_2 - w_1$ = $OE$. That's straight forward. Therefore point $E$ is $w_2 - w_1$.
$DA$ is a $\pi/2$ rotation anti-clockwise of AB, so $DA = i(w_2 - w_1)$. Therefore point $F$ is $i(w_2 - w_1)$.
I'm stuck on how to find point $C$ and $D$. I know (by substituting values for $w_1 = 4 + 2i$ and $w_2 = 8 + 5i$, say) that the answer for point $C$ is $w_2 + i(w_2 - w_1)$, but I can't see how to deduce this without 'hard coded' values.
Any help appreciated