Equilateral triangle and complex numbers

**The question:**

Show that the triangle in the complex plane whose verticies are the origin and the points $\displaystyle w_1$ and $\displaystyle w_2$ is equalateral if and only if $\displaystyle w_1^2 + w_2^2 = w_1w_2$

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.