There exist two different complex numbers $c_1$ and $c_2$, that together with $2+2i, 5+i$ form the vertices of two equilateral triangles. Find the product $c_1c_2$.
In the complex plane, this is just a simple geometry problem
So, two points of the triangle are (2,2) and (5,1).
The link below shows how to determine a third point given 2 points and the side lengths Hopefully with it you should be able to figure out the rest. Comment if you get lost so I can advise.