[ttoinou]

My definition of complex numbers : 2D points with multiplication such as you multiply their polar radius and add their polar angle (https://en.wikipedia.org/wiki/Polar_coordinate_system) and normal vector addition. (You can find back i=sqrt(-1) and all complex numbers properties / theorems after that of course)

For more visual explanations of complex numbers I recommend Tristan Needham's "Visual Complex Analysis" : http://pipad.org/tmp/Needham.visual-complex-analysis.pdf