Consider this formulation of complex numbers: Unit is 2x2 identity matrix. imaginary unit is the matrix -1 0 0 1 It is easy to check that imaginary

Consider this formulation of complex numbers: Unit is 2x2 identity matrix. imaginary unit is the matrix -1 0 0 1 It is easy to check that imaginary unit squared is -1. And addition and multiplication is just matrices. It then quickly becomes apparent that all possible matrices you generate _are_ the rotation and scaling matrices. Instead of drawing a connection between rotation and complex numbers, they all of a sudden are the same thing.