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# View of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers/ur_cn_1_32.pg

Tue Jul 17 17:17:39 2007 UTC (5 years, 10 months ago) by jjholt
File size: 2516 byte(s)
It's Snider, not Snyder.


    1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS ('complex','imaginary','root')
6 ## Tagged by cmd6a 4/20/06
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Complex Variables')
10 ## DBsection('Complex Numbers')
11 ## Date('')
12 ## Author('')
13 ## Institution('Rochester')
14 ## TitleText1('Complex Analysis')
15 ## EditionText1('3')
16 ## AuthorText1('Saff, Snider')
17 ## Section1('1.5')
18 ## Problem1('')
19
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
27 "PGauxiliaryFunctions.pl",
28 "PGcomplexmacros.pl"
29 );
30
31
32 TEXT(beginproblem());
33 $showPartialCorrectAnswers = 1; 34 35$s1 = random(-1,1,2);
36 if ($s1 == 1) {$pm1 = '+';}
37 else { $pm1 = '-';} 38 39$s2 = random(-1,1,2);
40 if ($s2 == 1) {$pm2 = '+';}
41 else { $pm2 = '-';} 42 43$r = random(2,10,1);
44
45 BEGIN_TEXT
46 Find all the values of the following :
47 $PAR 48 (1) $$(1 pm1 \sqrt{3}i)^\frac{1}{3}$$ 49$PAR
50 Place all answers in the following blank, separated by commas:
51 $PAR 52 \{ans_rule(80)\} 53$PAR
54 (2) $$(i pm2 1)^\frac{1}{2}$$
55 $PAR 56 Place all answers in the following blank, separated by commas: 57$PAR
58 \{ans_rule(80)\}
59 $PAR 60 (3) $$\displaystyle \left(\frac{r i}{1+i}\right)^\frac{1}{6}$$ 61$PAR
62 Place all answers in the following blank, separated by commas:
63 $PAR 64 \{ans_rule(80)\} 65 END_TEXT 66 67$a = new Complex( 2**(1/3)*cos($s1*$PI/9) , 2**(1/3)*sin($s1*$PI/9));
68 $b = new Complex( 2**(1/3)*cos(($s1+6)*$PI/9) , 2**(1/3)*sin(($s1+6)*$PI/9)); 69$c = new Complex( 2**(1/3)*cos(($s1+12)*$PI/9) , 2**(1/3)*sin(($s1+12)*$PI/9));
70 $d = new Complex( 2**(1/4)*cos((4+$s2)*$PI/8) , 2**(1/4)*sin((4+$s2)*$PI/8)); 71$f = new Complex( 2**(1/4)*cos((12+$s2)*$PI/8) , 2**(1/4)*sin((12+$s2)*$PI/8));
72 $g = new Complex(); 73$g = ($r*$r/2)**(1/12)*2.71828182845905**(i()*$PI/24); 74$h = new Complex();
75 $h = ($r*$r/2)**(1/12)*2.71828182845905**(i()*$PI*(1 + 1 * 8)/24);
76 $j = new Complex(); 77$j = ($r*$r/2)**(1/12)*2.71828182845905**(i()*$PI*(1 + 2 * 8)/24); 78$k = new Complex();
79 $k = ($r*$r/2)**(1/12)*2.71828182845905**(i()*$PI*(1 + 3 * 8)/24);
80 $l = new Complex(); 81$l = ($r*$r/2)**(1/12)*2.71828182845905**(i()*$PI*(1 + 4 * 8)/24); 82$m = new Complex();
83 $m = ($r*$r/2)**(1/12)*2.71828182845905**(i()*$PI*(1 + 5 * 8)/24);
84
85 ANS(multi_cmp( [ cplx_cmp($a), cplx_cmp($b), cplx_cmp($c) ] )); 86 ANS(multi_cmp( [ cplx_cmp($d), cplx_cmp($f) ] )); 87 ANS(multi_cmp( [ cplx_cmp($g), cplx_cmp($h), cplx_cmp($j), cplx_cmp($k), cplx_cmp($l), cplx_cmp(\$m)] ));
88
89 ENDDOCUMENT();        # This should be the last executable line in the problem.
90