PPT-Complex Numbers and Phasors

Outline Linear Systems Theory Complex Numbers Polyphase Generators and Motors Phasor Notation Reading Shen and Kong Ch 1 True False 1 In Lab 1 you built a motor about 5 cm in diameter If this motor spins at 30 Hz it is operating in the quasistatic regime. This is the basic theory behind how PSpice handles linear circuits and linear smallsignal approximations of nonlinear circuits Th e basic techniques are also widely used in many types of linear analysis found in physics and engineering ele ctrical o Electrical Science. Chapter 10: Sinusoidal Steady-State Analysis. Linear circuits with sinusoidal inputs that are at steady state are called ac circuits, . e.g. , the power system that provides us with electricity can be considered a very large ac circuit. Conjugate of a Complex Number…. The conjugate of a complex number . is . . . The conjugate of . is denoted . .. Find the conjugate of the following:. . . . .  . Using the Conjugate of a Complex Number. . John and Betty. . Betty and John. . One day John wanted to share 10 biscuits between Betty and himself..  . "How many should we each get?" he asked Betty.. . "Well, if we let . x. be the number of biscuits we each get then:. numbers. 1. Exponential Form:.  .  . Rectangular Form:. Real. Imag. x. y. f. r. =|z. |.  .  .  . The real and imaginary parts of a complex number in rectangular form are real numbers:. Real. Imag. The . imaginary . number . i. Simplifying square roots of negative numbers. Complex . Numbers, and their Form. The Arithmetic of Complex Numbers. Complex Conjugates. Division of Complex Numbers. Powers of . Introduction. This chapter extends on what you have learnt in FP1. You will learn how to find the complex roots of numbers. You will learn how to use De . Moivre’s. theorem in solving equations. You will see how to plot the loci of points following a rule on an . .. . Once a student knows the difference between the three sentence types (simple, compound, and complex), it is possible to write with sentence variety. Sentence variety helps make your writing more interesting.. What is a compound sentence?. A . compound sentence . has at least one . independent clause. ; . it is . usually two independent clauses joined by a semi-colon or a conjunction.. In other words, a . compound . Numbers. Abbreviations and Acronyms. Reference material:. American Psychological Association. (2010). . Publication manual of the American Psychological Association . (6. th. ed.). Washington, DC: Author. . 1.. 2.. 3.. 4.. 5.. f. (. x. ) = . x. 2. . – 18. x. + 16. f. (. x. ) = . x. 2. . + 8. x. – 24. Find the zeros of each function.. Define and use imaginary and complex numbers.. Solve quadratic equations with complex roots.. Maria Murphy. Central Florida Math Circle. University of Central Florida . Department of Mathematics . What is a Palindrome? . A palindrome is a word or phrase that reads the same forwards and backwards. . Complex Numbers. Recall that a complex number has a real component and an imaginary component.. z = a + bi. Argand Diagram. Real axis. Imaginary axis. z = 3 – 2i. z = 3 – 2i. a. bi. The absolute value of a complex number is its distance from the origin.. 1. Exponential Form:.  .  . Rectangular Form:. Real. Imag. x. y. f. r. =|z. |.  .  .  . The real and imaginary parts of a complex number in rectangular form are real numbers:. Real. Imag. x. =. Re(z).