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 none equal to zero.

are three complex numbers such that

http://latex.codecogs.com/gif.latex?...mma \right |=1

if , and http://latex.codecogs.com/gif.latex?...a y+\gamma z=0,

Prove that : http://latex.codecogs.com/gif.latex?...=\beta =\gamma