# Thread: proving right triangle with complex points

1. ## proving right triangle with complex points

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!

2. Originally Posted by morganfor
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!
These are just the same as point in $\displaystyle \mathbb{R}^2$

$\displaystyle 3+i=(3,1),6=(6,0),4+4i=(4,4)$

I hope this helps.

3. 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).