Classical control theory | Complex analysis | Complex numbers

Complex plane

In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the x-axis, called the real axis, is formed by the real numbers, and the y-axis, called the imaginary axis, is formed by the imaginary numbers. The complex plane allows a geometric interpretation of complex numbers. Under addition, they add like vectors. The multiplication of two complex numbers can be expressed more easily in polar coordinates—the magnitude or modulus of the product is the product of the two absolute values, or moduli, and the angle or argument of the product is the sum of the two angles, or arguments. In particular, multiplication by a complex number of modulus 1 acts as a rotation. The complex plane is sometimes known as the Argand plane or Gauss plane. (Wikipedia).

Complex plane
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What is the complex number plane

http://www.freemathvideos.com In this video series I will show you how to graph complex numbers by graphing a complex number on the imaginary and real axis. We will graph these just like we graph coordinate points but now with imaginary axis. Subscribe! http://www.freemathvideos.com Want

From playlist Simplify Rational Expressions

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Complex Numbers as Points (1 of 4: Geometric Meaning of Addition)

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From playlist Complex Numbers

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Some Basic Properties of Complex Numbers

This video describes some of the more basic properties of complex numbers.

From playlist Basics: Complex Analysis

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Circle in Complex Plane

Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook Determine and sketch the set of points in the complex plane that satisfied this equation here, now. let us just remind ourselves about a bit at the notation say, z is a complex number and in Cartesian form it is writt

From playlist Intro to Complex Numbers

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Complex Matrices ( An intuitive visualization )

Complex Matrices are not given enough credit for what they do and even when they are used its often introduced as an foreign entity. This video was made to shed light on such a misinterpreted topic. Timestamps 00:00 - Introduction 00:11 - Matrix 00:45 - Complex Number 02:50 - Complex Ma

From playlist Summer of Math Exposition Youtube Videos

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Part I: Complex Variables, Lec 3: Conformal Mappings

Part I: Complex Variables, Lecture 3: Conformal Mappings Instructor: Herbert Gross View the complete course: http://ocw.mit.edu/RES18-008F11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT Calculus Revisited: Calculus of Complex Variables

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What are complex numbers? | Essence of complex analysis #2

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From playlist Essence of complex analysis

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AlgTop4: More on the sphere

This lecture continues our discussion of the sphere, relating inversive geometry on the plane to the more fundamental inversive geometry of the sphere, introducing the Riemann sphere model of the complex plane with a point at infinity. Then we discuss the sphere as the projective line ove

From playlist Algebraic Topology: a beginner's course - N J Wildberger

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Visualizing simple complex functions -- Complex Analysis 3

Mathematica Notebook: https://bit.ly/3t0ONEg ⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn ⭐my other channels⭐ Main Channel: https://www.yout

From playlist Complex Analysis

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Visualizing the Fundamental Theorem of Algebra // Math Minute [#48]

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Imaginary Numbers Are Real [Part 6: The Complex Plane]

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Complex Analysis L04: The Complex Logarithm, Log(z)

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From playlist Engineering Math: Crash Course in Complex Analysis

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Weakly Modular Functions | The Geometry of SL2,Z, Section 1.4

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From playlist The Geometry of SL(2,Z)

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On Ultra-Parallel Complex Hyperbolic Triangle Groups by Anna Pratoussevitch

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Complex Analysis L08: Integrals in the Complex Plane

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From playlist Engineering Math: Crash Course in Complex Analysis

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Dividing Complex Numbers Example

Dividing Complex Numbers Example Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys

From playlist Complex Numbers

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