[npl] / trunk / NationalProblemLibrary / Rochester / setAlgebra11ComplexNumbers / ur_cn_1_34.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# View of /trunk/NationalProblemLibrary/Rochester/setAlgebra11ComplexNumbers/ur_cn_1_34.pg

Thu Aug 16 23:07:34 2007 UTC (5 years, 9 months ago) by jj
File size: 1504 byte(s)
Moved problems back into place in the Rochester library, and set up
redirect files from their former locations.


    1 ##KEYWORDS('algebra', 'complex number')
2 ## hcao tagged and PAID on 2-20-2004
3
4 ## DBsubject('Algebra')
5 ## DBchapter('Equations and Inequalities')
6 ## DBsection('Complex Numbers')
7 ## Date('6/3/2002')
8 ## Author('')
9 ## Institution('')
10 ## TitleText1('College Algebra')
11 ## EditionText1('3')
12 ## AuthorText1('Stewart, Redlin, Watson')
13 ## Section1('3.4')
14 ## Problem1('61')
15 ##DESCRIPTION
16 ##KEYWORDS('complex')
17 ##
18 ##ENDDESCRIPTION
19
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.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$BR
53 (a) $$k z =$$ \{ans_rule(10)\} $$+$$ \{ans_rule(10)\} $$i$$,
54 $BR 55 (b) $$\bar{z} =$$ \{ans_rule(10)\} $$+$$ \{ans_rule(10)\} $$i$$, 56$BR
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