The distance from the origin to is , the distance from the origin to is , and the distance from to is . For an equilateral triangle, those must all be equal.
The question:
Show that the triangle in the complex plane whose verticies are the origin and the points and is equalateral if and only if
I have a feeling that the reasoning behind this is quite simple. No matter what I've tried, I can't get the same result they do. Do I have to equate the distances between the vertices to be equal? Or is there some other property I should be exploiting? Thanks.
I remember seeing other solutions, and after searching I was surprised to find my own advice, which works in one direction. This problem was also discussed here and here.