View of /trunk/NationalProblemLibrary/ASU-topics/setComplexNumbers/srw3_4_23.pg

    1 ## DESCRIPTION
    2 ## Algebra of Complex Numbers
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('complex', 'imaginary')
    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 );
   37 
   38 TEXT(beginproblem());
   39 $showPartialCorrectAnswers = 1;
   40 
   41 $x1 = non_zero_random(-4,4,1);
   42 $y1 = non_zero_random(-4,4,1);
   43 $x2 = non_zero_random(-4,4,1);
   44 $y2 = non_zero_random(-4,4,1);
   45 
   46 $a = $x1*$x2-$y1*$y2;
   47 $b = $x1*$y2+$x2*$y1;
   48 
   49 $c1=nicestring([$x1,$y1],['','i']);
   50 $c2=nicestring([$x2,$y2],['','i']);
   51 
   52 #c1 = x1 + y1 i
   53 #c2 = x2 + y2 i
   54 
   55 TEXT(EV2(<<EOT));
   56 Evaluate the expression \( ($c1)($c2)\) and
   57 write the result in the form \(a+ b i\).
   58 $BR $BR
   59 The real number \(a\) equals \{ans_rule(15) \}
   60 $BR
   61 The real number \( b \) equals \{ans_rule(15) \}
   62 $BR
   63 EOT
   64 
   65 $ans1 = $a;
   66 $ans2 = $b;
   67 ANS(num_cmp($ans1));
   68 ANS(num_cmp($ans2));
   69 
   70 ENDDOCUMENT();        # This should be the last executable line in the problem.
   71