View of /trunk/NationalProblemLibrary/ASU-topics/setComplexNumbers/beth1complex.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 "PGcomplexmacros.pl"
   35 );
   36 
   37 TEXT(beginproblem());
   38 $showPartialCorrectAnswers = 1;
   39 
   40 $x1 = non_zero_random(-4,4,1);
   41 $y1 = non_zero_random(-4,4,1);
   42 $x2 = non_zero_random(-4,4,1);
   43 $y2 = non_zero_random(-4,4,1);
   44 $c = non_zero_random(-6,6);
   45 
   46 $b = ($x1*$x2*$c+$y1*$y2*$c)/($x2**2+$y2**2);
   47 $a = (-$x1*$y2*$c+$x2*$y1*$c)/($x2**2+$y2**2);
   48 
   49 BEGIN_TEXT;
   50 Evaluate the expression
   51 \[ \frac{($x1 - $y1 i)($c i)}{$x2 - $y2 i}\]
   52 and write the result in the form \(a+ b i\).
   53 $BR
   54 Then \(a = \) \{ans_rule(10)\} and \(b = \) \{ans_rule(10)\}
   55 
   56 END_TEXT
   57 
   58 
   59 
   60 ANS(num_cmp($a));
   61 ANS(num_cmp($b));
   62 
   63 
   64 ENDDOCUMENT();        # This should be the last executable line in the problem.
   65