Real Life Applications of Imaginary Numbers

• Complex numbers enter into studies of physical phenonomena in ways that most people can't imagine.

• For example: A differential equation, with coefficients like the a, b, and c in the quadratic formula, that models how electrical circuits or forced spring/damper systems behave. The movement of the shock absorber of a car as it goes over a bump is an example of the latter. The behavior of the differential equations depends upon whether the roots of a certain quadratic are complex or real. If they are complex, then certain behaviors can be expected. These are often just the solutions that one wants.

• Closely related to the electrical engineering example is the use of complex numbers in signal processing, which has applications to telecommunications (cellular phone), radar (which assists the navigation of airplanes), and even biology (in the analysis of firing events from neurons in the brain).

• In modeling the flow of a fluid around various obstacles, like around a pipe, complex analysis is very valuable for transforming the problem into a much simpler problem. When everything from large structures of riveted beams to economic systems are analyzed for resilience, some very large matrices are used in the modeling.

• In everyday use, industrial and university computers spend some fraction of their time solving polynomial equations. The roots of such equations are of interest, whether they are real or complex