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.
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.