'Real part' diaporamas de présentation

Complex Numbers 2

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Chapter 2 Response to Harmonic Excitation

Chapter 2 Response to Harmonic Excitation. Introduces the important concept of resonance. 2.1 Harmonic Excitation of Undamped Systems. Consider the usual spring mass damper system with applied force F ( t )= F 0 cos w t w is the driving frequency F 0 is the magnitude of the applied force

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AC Circuit Theory

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PROGRAMME 1

PROGRAMME 1. COMPLEX NUMBERS 1. Programme 1: Complex numbers 1. Introduction The symbol j Powers of j Complex numbers Equal complex numbers Graphical representation of a complex number Graphical addition of complex numbers Polar form of a complex number

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A long long time ago, in a math class far, far away..

A long long time ago, in a math class far, far away. There was no way to take the square root of a negative number. Every time we squared a negative number. We got a positive. (-1) = 1 (-2) = 4 (-3) = 9. Is there a number, that when multiplied by itself. gives you a negative???.

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259 Lecture 10 Spring 2013

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MAC 1105

MAC 1105. Module 11 Solution of Polynomial Equations. Rev.S08. Learning Objective. Upon completing this module, you should be able to: Solve polynomial equations using factoring. Solve polynomial equations using factoring by grouping. Solve polynomial equations using the root method.

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Polynomials Review and Complex numbers

Warm Up Problem: The game of assassin is played with 8 people and goes as follows: Each player is somehow assigned a target. You attempt to assassinate your target. if you succeed, you inherit the current target of the person you just killed If you fail, you are removed from the game

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Benjamin D. Braaten* North Dakota State University, Fargo ND, USA David A. Rogers

Current Distribution of a Printed Dipole with Arbitrary Length Embedded in Layered Uniaxial Anisotropic Dielectrics. Benjamin D. Braaten* North Dakota State University, Fargo ND, USA David A. Rogers North Dakota State University, Fargo ND, USA Robert M. Nelson

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J. McCalley

J. McCalley. Machine Transformations. Consider a 2-pole induction machine with the a-phase stator winding, having N a turns, is distributed about its axis as shown below. Space vectors. The conductor density of the phase a winding is.

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Finding Eigenvectors

Finding Eigenvectors. Some Examples. General Information. Eigenvalues are used to find eigenvectors. The sum of the eigenvalues is called the trace. The product of the eigenvalues is the determinant of the matrix.

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Solving Differential Equations

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Fading

Fading. Kevin Bolding Electrical Engineering Seattle Pacific University. Signals fade . Received Signal Strength (RSS) varies over time and space Slow Fading caused by large obstacles and terrain impairments Appears as local rises/falls in RSS around a logarithmic curve. Multipath fading.

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Complex Numbers

Complex Numbers. Complex Numbers. The imaginary unit i is defined as. Example. Complex Numbers. The set of all numbers in the form a + b i with real numbers a and b , and i , the imaginary unit, is called the set of complex numbers.

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Complex Numbers 1-5

Complex Numbers 1-5. Kayla McGoran, Allie Gloor, Megan White, and Sarah Kidder. Real Numbers. Real Numbers are used for measurement and that can be represented on a continuous number line.

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Matlab Tutorials

Matlab Tutorials. 10 / 04 / 2006. Introduction to Matlab Working with Matlab Image Processing using Matlab Class Project. Introduction. MatLab : Mat rix Lab oratory Numerical Computations with matrices Every number can be represented as matrix Why Matlab? User Friendly (GUI)

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1-10 Introduction to Complex Numbers

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Complex Numbers

Complex Numbers. Adding in the Imaginary i. By Lucas Wagner. The Domain of the Square Root. We might think of as a parabola on its side, with the following equivalent statement:. So we can see that negative values of x do not yield any real y -values. . The Quadratic Formula.

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Writing complex numbers

Writing complex numbers. Unit 1: topic 3. VOCABULARY. Square root: A number r is a square root of a number if r 2 = s Radical: the symbol ? is a radical sign Radicand: the number beneath the radical sign Imaginary unit i : defined as i = ?-1 i 2 = -1. VOCABULARY.

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The History of Imaginary Numbers

The History of Imaginary Numbers. Wilfredo Salazar. Gerolamo cardano . In his exposition in 1545,acknowledged the existence of what are now called imaginary numbers. Although he did not understand their properties, mathematical field theory was developed centuries later . .

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