I found a simple but interesting problem which can be solved using highschool concepts regarding complex numbers... (I posted it here since it's purely optional, those interested may try.)

Consider three real numbers $\displaystyle x,y,z$ none equal to zero.

$\displaystyle \alpha,\beta,\gamma$ are three complex numbers such that

if $\displaystyle x+y+z=0$ , and ,

Prove that :