I highly recommend Brian's visualization -- another way to see the identity is to imagine e^ix as a spiral that gets tighter and tighter as you compound more fr

I highly recommend Brian's visualization -- another way to see the identity is to imagine e^ix as a spiral that gets tighter and tighter as you compound more frequently (e represents infinite compounding). This formula has so many cool interpretations, yet is often explained by resorting to Taylor series (which is like comparing the equations molecule-by-molecule instead of seeing the big picture).