Imaginary to Physical Mapping "Contrary to its name, the Imaginary Number exists in a similar fashion to the Real number, often describing physical characteristics that we can detect, observe, and measure." (picomonster.com)
Imaginary numbers are used for a variety of things. Complex calculus is used to find real solutions such as rates of change in the flow of a fluid, magnetic field, heat, sound, and gravity.
Complex numbers are used by engineers who use it for circuit analysis and vibration analysis. They use it to study stresses on beams and to study resonance.
Imaginary numbers are used in electric circuits and help in transmitting radio waves.
Imaginary numbers are used in climate modeling. By using complex calculus, we are able to solve problems in the most efficient ways. Without using this technique modern computers wouldn't even be able to solve these problems because it would take so long.
Imaginary numbers are used with digital cameras. The fourier transform breaks down a periodic functions into a set of simple oscillating functions which are complex exponentials. This fourier transform is used to compress information in a picture to a memory card of a digital camera.
Imaginary numbers are used in quantum physics which describes our world.