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Tue Jul 3 17:27:24 2007 UTC (5 years, 10 months ago) by jjholt
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Updated Tags.  --JJH


    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('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
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 "PGgraphmacros.pl",
28 "PGmatrixmacros.pl",
29 "PGnumericalmacros.pl",
30 "PGauxiliaryFunctions.pl"
31 );
32
33 TEXT(beginproblem());
34 $showPartialCorrectAnswers = 1; 35 36$a = non_zero_random(-9,9,1);
37 $b = non_zero_random(-9,9,1); 38 if ($b == $a) {$b = 10; }
39
40 $k = random(2,9,1)*random(-1,1,2); 41 42$ans1 = $k*$a;
43 $ans2 =$k*$b; 44$ans3 = $a; 45$ans4 = - $b; 46$ans5 = $a/($a*$a +$b*$b); 47$ans6 = - $b/($a*$a +$b*$b); 48 49 BEGIN_TEXT 50 51 Let $$z = a + b i$$. Write the following numbers in $$a+bi$$ form: 52$PAR
53 (a) $$k z =$$ \{ans_rule(10)\} $$+$$ \{ans_rule(10)\} $$i$$,
54 $PAR 55 (b) $$\bar{z} =$$ \{ans_rule(10)\} $$+$$ \{ans_rule(10)\} $$i$$, 56$PAR
57 (c) $$\displaystyle \frac{1}{z} =$$ \{ans_rule(10)\} $$+$$ \{ans_rule(10)\} $$i$$.
58
59 END_TEXT
60
61 ANS(num_cmp($ans1)); 62 ANS(num_cmp($ans2));
63 ANS(num_cmp($ans3)); 64 ANS(num_cmp($ans4));
65 ANS(num_cmp($ans5)); 66 ANS(num_cmp($ans6));
67
68 ENDDOCUMENT();       # This should be the last executable line in the problem.
69


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