Since complex numbers provide a system for finding the roots of polynomials, and polynomials are used as theoretical models in various fields, complex numbers enjoy prominence in several specialized areas. Among these specialized areas are engineering, electrical engineering and quantum mechanics. Topics utilizing complex numbers include the investigation of electrical current, wavelength, liquid flow in relation to obstacles, analysis of stress on beams, the movement of shock absorbers in cars, the study of resonance of structures, the design of dynamos and electric motors, and the manipulation of large matrices used in modeling. While many of these applications are beyond the scope of an Algebra2/Trig curriculum, an introductory glimpse of the application of complex numbers to electrical circuits can be easily understood and manipulated by students.
Possible Student Questions:
Hopefully, this will help to answer the question "Does anyone ever really use complex numbers?"