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 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. Numbers. Once upon a time…. Complex Number System.  . Reals. Rationals. (Can be written as fractions). Integers. (…, -1, -2, 0, 1, 2, …). Whole. (0, 1, 2, …). Natural. (1, 2, …). Irrationals. Raymond Flood. Gresham Professor of Geometry. Hamilton, Boole and their Algebras. George Boole 1815–1864. .  . William Rowan Hamilton 1805–1865. .  . William Rowan Hamilton 1805. –. 1865. William Rowan Hamilton 1805. 06.10.2011. 2.2. . Sinusoids. A sinusoids is signal that has the form of the . sine. or . cosine. function.. Consider the sinusoidal voltage.. 2.2. . Sinusoids. as a . function. of . ω. t. as a . . 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:. Definitions. Conversions. Arithmetic. Hyperbolic Functions. Main page. Argand diagram. Im. . Re . If the complex number then . the . Modulus. of is written as and . the . Argument . 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 . , Capacitors, Impedance. Spin My World Right Round. LPF Application: Gastric Electrical Activity. 60-70 million people suffer from GI disorder. Electrically active organ. http://www.virtualmedicalcentre.com/anatomy/gastrointestinal-system/7. Danville Senior Center. May 5, 2016. The plan…sort of…. A seminar, not a class.. I have an “agenda”, but we can ignore . it.. But let’s start with introductions-and maybe include your math background and interests.. 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.. Argand. diagram. Each marking on the axes represents one unit.. . 2.. Plot the following complex numbers on an . Argand. diagram:. . (. i. ) 3 + 2. i. . (ii) −1 − 5. i. . (iii) −4 + . i. . 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).