let A and B be two complex number such that A/B+B/A =1 prove that the origin and the two points represented by A and B form vertices of an equilateral triangle

The triangle with origin, A and B as vertices will have side lengths |A|, |B| and |A-B|.

We will prove that |A| = |B| = |A-B|.

Similarly 

From the above two relations we immediately obtain that 

Hence,