- 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

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