Geometry Question - Complex numbers & triangles

AI Thread Summary
The discussion centers on finding complex numbers for the vertices of triangle ABC based on the midpoints of its sides, represented by complex numbers z_1, z_2, and z_3. The initial confusion involves the choice of the origin, with a suggestion that placing it at vertex A leads to vertices B and C being represented as 2*z_3 and 2*z_2, respectively. However, it is clarified that the origin's location is irrelevant to the problem, as the focus is on similar triangles. The realization emphasizes that the relationship between the midpoints and vertices remains consistent regardless of the origin. The conversation highlights the importance of understanding the properties of complex numbers in geometric contexts.
MattL
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OK, I've got this question to do:

Find complex numbers representing the vertices of a triangle ABC given
that the midpoints of the sides BC, CA, AB are represented by complex numbers
z_1, z_2, z_3 respectively.

Thing is, I don't know where I'm taking the origin to be; if I took it at A then I would just have A is O, B is 2*z_3, C is 2*z_2. Surely there's more to the question than that?
 
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yeah, oops, just realized it's about similar triangle and it doesn't matter where the origin is...
 
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