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Math Help - proving right triangle with complex points

  1. #1
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    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!
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  2. #2
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    Quote Originally Posted by morganfor View Post
    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 \mathbb{R}^2

    3+i=(3,1),6=(6,0),4+4i=(4,4)

    I hope this helps.
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  3. #3
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    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).
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