View of /trunk/NationalProblemLibrary/ASU-topics/setComplexNumbers/zhu8.pg

    1 ## DESCRIPTION
    2 ## Imaginary Roots of Quadratics
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('complex', 'imaginary', 'quadratic', 'root')
    6 ## Tagged by YL
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Complex Variables')
   10 ## DBsection('Complex Numbers')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('Calculus: Early Transcendentals')
   15 ## EditionText1('5')
   16 ## AuthorText1('Stewart')
   17 ## Section1('G')
   18 ## Problem1('')
   19 
   20 ## TitleText2('Calculus: Early Transcendentals')
   21 ## EditionText2('6')
   22 ## AuthorText2('Stewart')
   23 ## Section2('G')
   24 ## Problem2('')
   25 
   26 DOCUMENT();        # This should be the first executable line in the problem.
   27 
   28 loadMacros(
   29 "PG.pl",
   30 "PGbasicmacros.pl",
   31 "PGchoicemacros.pl",
   32 "PGanswermacros.pl",
   33 "PGauxiliaryFunctions.pl",
   34 "PGasu.pl",
   35 "extraAnswerEvaluators.pl",
   36 "PGcomplexmacros.pl"
   37 );
   38 
   39 TEXT(beginproblem());
   40 $showPartialCorrectAnswers = 1;
   41 
   42 $b =  non_zero_random(-4,4,1);
   43 $c =  random(5,8,1);
   44 
   45 $p=nicestring([1,$b,$c]);
   46 
   47 TEXT(EV2(<<EOT));
   48 Find all solutions of the equation \( $p = 0\) and
   49 express them in the form \(a + b i\):
   50 $BR $BR
   51 First input the solution with \(b <0\) here:
   52 $BR
   53 
   54  \{ans_rule(25) \}
   55 $BR
   56 Then input the solution with \(b > 0\) here:
   57 $BR
   58 
   59  \{ans_rule(25) \}
   60 $BR
   61 EOT
   62 
   63 $nb=-$b;
   64 $delta=-$b**2+4*$c;
   65 $ans1 = $nb/2;
   66 $ans2 = ($delta)**0.5/2;
   67 $ans3 = $nb/2;
   68 $ans4 = ($delta)**0.5/2;
   69 
   70 ANS(number_list_cmp("$ans1-$ans2 i",complex=>'ok'));
   71 
   72 ANS(number_list_cmp("$ans3+$ans4 i",complex=>'ok'));
   73 
   74 
   75 ENDDOCUMENT();        # This should be the last executable line in the problem.
   76