The derivative of e^ix is ie^ix. Multiplication by i is equivalent to rotation by 90 degrees. The derivative of velocity is acceleration. Acceleration perpendic

The derivative of e^ix is ie^ix. Multiplication by i is equivalent to rotation by 90 degrees. The derivative of velocity is acceleration. Acceleration perpendicular to velocity is circular motion. With base 2 the motion is not circular. All these pieces (and an initial value problem differential equation) come together to explain the identity.