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Unformatted text preview: 18.03 Problem Set 3 Spring 2009 Due in boxes at Room 2106, 12:55 pm, Friday, Feb 20 Part A (16 points) (at due date) Write the names of any person, web site, or materials you consulted. Write “No C” (no consultation) on your paper if you consulted no fellow students, outside mate rials/people. Lec 5, Fri, Feb 13; Complex numbers; complex exponentials. Read: C.13, Work: 2E1, 2, 7, 14, 16b Lec 6, Tue, Feb 17; More about exponentials; Roots of unity Read: C.4, IR.6 Work: 2E9,10 Lec 7, Wed, Feb 18; Linear response to exponential and sinusoidal input. Read: IR.13, 5; Work: 2E15 Lec 8, Fri, Feb 20; Autonomous equations, phase line, stability. Read: EP 1.7, 7.1 Part B (32 points) 1. (Lec 5, Fri, Feb 13) [9pts: 2,2,1,2,2] Complex numbers; polar representation a) Express 2 / (1 + i ) as a + bi and as re iθ where a , b , r > 0, and θ are real numbers. b) Find the real an imaginary parts of e 2 πi and e 2+ πi/ 2 . c) Suppose that z 3 = 1 and z 6 = 1. Show that z 2 + z + 1 = 0 using algebra. d) Do part (c) again by a more circuitous method. i) Find the polar representations for the two root of z 3 = 1 with z 6 = 1, and use this to find the rectangular representations (the form...
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This note was uploaded on 05/06/2010 for the course 18 18.03 taught by Professor Unknown during the Spring '09 term at MIT.
 Spring '09
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