Imaginary Numbers In The "Real World".
"Practical" has a different meaning to everyone. Since numerous applications are based on polynomial models in theory, complex numbers play a part in all of these. For example, in electrical engineering we find complex roots in circuit theory where the polynomial is part of the model equation for simple circuits. In mechanical engineering, the same type of model relates to vibrations with wavelike results connected to the complex root cases. And in physics, it turns out quantum mechanics uses complex numbers for just about everything - the wave functions of particles have a complex amplitude, including a real and "imaginary" part, and both are essential. From the perspective of algebra, complex numbers give us a complete system for finding the roots of polynomials. The two really go hand in hand.
Even more so, however, the medical field makes use of imaginary numbers. In the modern hospital, the storage of electronically recorded data is an important goal. For instance, the efficient coding of "ECGs" enables more data to be stored on "Holter-devices", which record the ECG for long periods. It also extends the capabilities of automatic defibrillators, which record the ECG sequence that triggered a defibrillation action. .
Efficient transmission of data and signals over telephone lines or mobile devices is also becoming more and more important. Remote diagnosis is important to patients in stuck remote areas, where the help of better doctors is not really available. Transmission of patient information from ambulances saves valuable time in emergencies and allows a physician at the hospital to provide better instructions to ambulance personnel. .
Because telephone lines and radio channels have low capacity, they can carry only a limited number of signals unless these signals are coded efficiently. For this purpose, we have developed several signal compression methods, which utilize polynomials and imaginary numbers.