i have to prove that a triangle is a right triangle given these points: 3+i, 6, and 4+4i. I know if you show that two lines have perpendicular slope that proves it but I don't understand how to do it with complex points. Thank you!
In the complex plane, multiplication by i has the effect of rotation through a right angle. If the complex numbers u,v,w represent the vertices of a triangle then the side from u to v is represented by the number v–u. So the condition for the angle at u to be a right angle is that w–u should be a real multiple of i(v–u).