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

    1 ##DESCRIPTION
    2 ##  Algebra problem: complex numbers
    3 ##ENDDESCRIPTION
    4 
    5 ##KEYWORDS('algebra', 'quadratic equation')
    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 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.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