Imaginary numbers just have an unfortunate name. The complex numbers (having a real and imaginary component) are objects on a 2-dimensional plane. Using complex numbers lets you describe, in algebraic terms, geometric entities and operations. Adding a+bi is translation. Multiplying by i is rotation by 90˚ counterclockwise. Multiplying by a, a real valued scalar, is scaling. Multiplying by bi is rotation and scaling. Multiplying by a+bi is rotation and scaling again, but the angle of rotation will be something other than 90˚.

The complex number notation describes an object in space or an action to be performed on objects in space. Other than it being more compact, it's not substantively different than a statement describing an action like "travel 50m northeast, then turn left, then travel 40m".