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# View of /trunk/NationalProblemLibrary/Rochester/setAlgebra11ComplexNumbers/sw3_4_55.pg

Thu Aug 16 23:07:34 2007 UTC (5 years, 10 months ago) by jj
File size: 1440 byte(s)
Moved problems back into place in the Rochester library, and set up
redirect files from their former locations.


    1 ##DESCRIPTION
2 ##  Algebra problem: complex numbers
3 ##ENDDESCRIPTION
4
6 ## tsch tagged and PAID on 12-12-2003
7
8 ## DBsubject('Algebra')
9 ## DBchapter('Equations and Inequalities')
10 ## DBsection('Complex Numbers')
11 ## Date('6/3/2002')
12 ## Author('')
13 ## Institution('')
14 ## TitleText1('College Algebra')
15 ## EditionText1('3')
16 ## AuthorText1('Stewart, Redlin, Watson')
17 ## Section1('3.4')
18 ## Problem1('55')
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 );
29
30 TEXT(beginproblem());
31 $showPartialCorrectAnswers = 1; 32 33$b =  random(2,4,1);
34 $c = random(5,8,1); 35 36 TEXT(EV2(<<EOT)); 37 Find all solutions of the equation $$t + b + \frac{c}{t} = 0$$ and 38 express them in the form $$a + b i$$: 39$BR $BR 40 First input the solution with $$b <0$$ here: 41$BR
42 the real number $$a$$ equals \{ans_rule(20) \}
43 and the real number $$b$$ equals \{ans_rule(20) \}
44 $BR 45 Then input the solution with $$b > 0$$ here: 46$BR
47 the real number $$a$$ equals \{ans_rule(20) \}
48 and the real number $$b$$ equals \{ans_rule(20) \}
49 $BR 50 EOT 51 52$ans1 = -$b/2; 53$ans2 = -(-$b**2+4*$c)**(1/2)/2;
54 $ans3 = -$b/2;
55 $ans4 = (-$b**2+4*$c)**(1/2)/2; 56 57 ANS(num_cmp($ans1));
58 ANS(num_cmp($ans2)); 59 ANS(num_cmp($ans3));
60 ANS(num_cmp(\$ans4));
61
62 ENDDOCUMENT();        # This should be the last executable line in the problem.
63