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EE20-2007-09-13-Quiz-01-SOL

EE20-2007-09-13-Quiz-01-SOL - EECS 20N Structure and...

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Unformatted text preview: EECS 20N: Structure and Interpretation of Signals and Systems QUIZ 1 Department of Electrical Engineering and Computer Sciences 13 September 2007 UNIVERSITY OF CALIFORNIA BERKELEY LAST Name ML FIRST Name W LabTime 368‘ 6:2 as to 4 0/.-- o (5 Points) Print your name and lab time in legible, block lettering above. o This quiz should take up to 20 minutes to complete. You will be given at least 20 minutes, up to a maximum of 30 minutes, to work on the quiz. 0 This quiz is closed book. Collaboration is not permitted. You may not use or access, or cause to be used or accessed, any reference in print or elec- tronic form at any time during the quiz. Computing, communication, and other electronic devices (except dedicated timekeepers) must be turned off. Noncompliance with these or other instructions from the teaching staff- including, for example, commencing work prematurely or continuing beyond the announced stop time—is a serious violation of the Code of Student Conduct. 0 We will provide you with scratch paper. Do not use your own. 0 The quiz printout consists of pages numbered 1 through 4. When you are prompted by the teaching staff to begin work, verify that your copy of the quiz is free of printing anomalies and contains all of the four numbered pages. If you find a defect 1n your copy, notify the staff immediately. 0 Please write neatly and legibly, because if we can’t read it, we can’t grade it. o For each problem, limit your work to the space provided specifically for that problem. No other work will be considered in grading your quiz. No exceptions. 0 Unless explicitly waived by the specific wording of a problem, you must ex- plain your responses (and reasoning) succinctly, but clearly and convincingly. 0 We hope you do a fantastic job on this quiz. 1—— Your S—orel |--—l l-I-l Q1.1 (20 Points) For each set defined below, provide a well—labeled diagram iden- tifying all the points on the complex plane that belong to it. The symbol C denotes the set of complex numbers. To receive full credit, you must explain your reasoning succinctly, but clearly and convincingly. You may tackle each part independently. (a) (10 Points) A={zEC|O.5$ |z—z'| g1}. Z-t- [5 fixe vecl'gr from Z 1‘0 2. \Z'L‘l (3 "TR: Mmanl “he, of TR: vhf/hr {Tomi l’o Z~ TR; Scl’ A ConslS—k; ol' CV‘CFa, F°lvx Z “W let Compkx flame Tim-lb no c\o$Cr‘ f0 1 mm 0.? anti mo )C’Arl-Exer JFroml‘l' WM 1. Huck is, eu<r& dame/Cl, 0+ A is o. poi/\‘\'9~A Rx: Comp\fix ‘3\°“"Q “f A ”Whovk exisl’oxmcCSNJDJ—Qten 0.3-, «1an l {Tom L &L 15‘; 0.? L A c 1% Surat mam Kc (bownlanfes off Text Omnw inf Ftalafl‘lac‘mclevb (b) (10 Points) B={zE<C||z—i|=|z+i|}. lg 18 ‘Wx: SC." 0'3; Wm ‘34le on The Comfltx \b\0\n€ TLWJV N‘t CWw‘wkS—l’owd/ {Tom {— OWVJ “L: C\ej\r\ ,‘ E =1 K) TE‘C Sink, a“; {taxi “WMLQPS (me )Q “US on 1R6. Complex f’vxnfi Skovdfl below) ,, . . B Q12 (20 Points) Consider the quartic (fourth-order) equation 24—422+16=0. (a) (16 Points) Determine the four solutions (roots) of the equation, and express each root in both a simple rectangular and a simple polar form. Explain your work succinctly, but clearly and convincingly. Your trigonometry teacher rightfully used to insist that cos(7r / 3) = sin(7r / 6) = V 1/2 and sin(1r/3) = cos(7r/6) = «5/2. 5°\Vt {ix 4530 files 8 : (13 Lej' x2292 «Ml convert We Twod‘tc C maxi/:0“ :rx 0 °\ o‘cwflglroj'cc gag) “kick FooltkC€$ +vdo coals“ X‘))(Pz‘.) ““4 (fl\—K\<fi. lee 5 «AFC “mu-\‘Ko’g’ QWC\’\ 0+ )(\ ”\“A X92 h «N‘NQ «'\’ A“ T62 ‘g’owr (‘oo'\'s A" Tea Ctv‘kKr‘RC-CTKXOA . ‘ , (I) W2 4;» {Emma—,0 =5 x:;:\/L+-\c,—.;z:szf’§t $5 - i - —' 'T' [V . dzrrazfi. mu; _ H/s . 3 x\:‘9~‘\’a‘l—§ L =\(",e a =Ll', e 3976’“ —:;§x\-.R+2\EL=FI-c S _ .-['\r \Ml\0\(\6) X92- (1-35 L 1 e /3 {K} 22“— K —§ z— Ll ~ —x v4 n? x c s wart A 1 We 2W 11m M1,, ML (kez) n x\ ml MM! 7% ' J ”‘0‘ F \ 1(13E’r—2Wk Z1 LEE—flat (‘00 S L evwlwmj—lfl “V [(10 l X:L‘-e __>x :02 _ , S \\ fl/ [.Efi'kV» ‘ z a (“/4 ”717“: Q "*2"; M X 2 M = e 1 : \ mama) ,2 at (o . ”it ngrr‘ool? are; c #175 22 Qe [251% e (b) (4 Points) Identify the four solutions as points on a single, well-labeled dia- _, gram of the complex plane. _£_ . l. “/63 a,“ Z\=\/$ ‘\" L '1 2C ...— If“ . [24L 4% Zgzefi- L :3: =2: 41% A“ {’mr Foal/S 5+ 0’1 7ft Cine/‘6 0)‘: fat/II‘LLS 02) CCVJEK‘CJ 47' fife amino. You may use this page for scratch work only. “Ethout exception, subject matter on this page will not be graded. ...
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