# Complex numbers in control theory

• ## What are complex numbers in set theory?

Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”.
The value of i = (√-1).
For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im)..

• ## What is set of complex numbers in set theory?

A complex number is a number that can be written in the form a + b i a + bi a+bi, where a and b are real numbers and i is the imaginary unit defined by i 2 = − 1 i^2 = -1 i2=−1.
The set of complex numbers, denoted by C, includes the set of real numbers (R) and the set of pure imaginary numbers..

• Mechanical & Structural Engineers use complex numbers to analyse the vibration of structures in machines, buildings and bridges, the behaviour of fluid flow around aircraft, and that of wind around buildings and bridges, preventing failures such as the Tacoma Narrows Bridge (Please watch the following video).
Complex numbers allow us to describe the properties of dynamic systems from the point of view of frequency. This analysis can be done by using the idea of the spectral transfer function, which is obtained from the transfer function by replacing the complex variable “s” by “jω”.

Study of strategic decision making

Mean-field game theory is the study of strategic decision making by small interacting agents in very large populations.
It lies at the intersection of game theory with stochastic analysis and control theory.
The use of the term mean field is inspired by mean-field theory in physics, which considers the behavior of systems of large numbers of particles where individual particles have negligible impacts upon the system.
In other words, each agent acts according to his minimization or maximization problem taking into account other agents’ decisions and because their population is large we can assume the number of agents goes to infinity and a representative agent exists.

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Complex numbers in field theory
Complex numbers and graph theory
Complex number theory
What are complex numbers
Complex number times complex number
What numbers are complex numbers
Concept of complex numbers
3-3 practice complex numbers
Complex numbers explained
Number theory for complex numbers
Complex numbers examples
Factor complex numbers
Complex numbers in number theory
Complex numbers in quantum theory
Complex numbers exercises
Logarithme complexe
Non complex numbers
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Complex numbers in nature
Theory of complex numbers