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


    1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS ('complex','imaginary')
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('1.3')
18 ## Problem1('')
19
20 DOCUMENT();        # This should be the first executable line in the problem.
21
22 loadMacros(
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
26 "PGanswermacros.pl",
27 "PGauxiliaryFunctions.pl",
28 "PGcomplexmacros.pl"
29 );
30
31 TEXT(beginproblem());
32 $showPartialCorrectAnswers = 1; 33 34$a = new Complex( non_zero_random( 1, 4, 1 ), non_zero_random(1,4,1));
35 $b = new Complex( non_zero_random( -4, -1, 1 ), non_zero_random( -4, -1,1)); 36 #$c = new Complex( non_zero_random( 1, 4, 1 ), non_zero_random(1,4,1));
37 $d = new Complex( non_zero_random( 1, 4, 1 ), non_zero_random(-4,-1,1)); 38$e = new Complex( non_zero_random( 1, 4, 1 ), non_zero_random(-4,-1,1));
39 $f = new Complex( non_zero_random( 1, 4, 1 ), non_zero_random(1,4,1)); 40$g = new Complex( non_zero_random( 1, 4, 1 ), non_zero_random(-4,-1,1));
41
42 BEGIN_TEXT
43
44 Calculate:$PAR 45 (a) $$\displaystyle \Big| \frac{a}{b} \Big|\ =$$ \{ans_rule(20)\},$PAR
46 (b) $$\displaystyle \Big| \overline{(1\ +\ i)}(d)(e)\Big|\ =$$ \{ans_rule(20)\}, $PAR 47 (c) $$\displaystyle \Big|\frac{i(f)^3}{(g)^2}\Big|\ =$$ \{ans_rule(20)\},$PAR
48 (d) $$\displaystyle \Big| \frac{(\pi\ + i) ^{100}}{(\pi\ -\ i)^{100}}\Big|\ =$$ \{ans_rule(20)\}.
49
50 END_TEXT
51
52 $i = new Complex( 0,1); 53$pi = 3.14159265359;
54
55 ANS(num_cmp( (($a)/($b) ) -> abs ));
56 ANS(num_cmp( ((1-$i)*($d)*($e)) -> abs ) ); 57 ANS(num_cmp( ($i*($f)**3 / ($g)**2 ) -> abs ) );
58 ANS(num_cmp( ((($pi +$i )**100)/(($pi -$i)**100))-> abs ) );
59
60
61 ENDDOCUMENT();        # This should be the last executable line in the problem.
62


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