How do complex numbers actually apply to control systems?

The video tutorial explores the application of Euler's formula in solving geometry puzzles using complex numbers. It introduces the Nyquist stability criterion, explaining its significance in control systems. The tutorial delves into complex functions and contours, illustrating their behavior in the complex plane. Finally, it discusses the application of these concepts in control systems, emphasizing stability analysis and feedback mechanisms.

What is the effect of adding a constant to a complex function in terms of its zeros?

Discuss the significance of poles and zeros in the context of complex functions and their stability.

What is the relationship between the number of rotations around the origin and the number of zeros and poles in a contour?

Explain how feedback can stabilize a system that is otherwise unstable due to its poles.