View of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers/ur_cn_1_34.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS ('complex','imaginary')
    6 ## Tagged by cmd6a 4/20/06
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Complex Variables')
   10 ## DBsection('Complex Numbers')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   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 "PGgraphmacros.pl",
   28 "PGmatrixmacros.pl",
   29 "PGnumericalmacros.pl",
   30 "PGauxiliaryFunctions.pl"
   31 );
   32 
   33 TEXT(beginproblem());
   34 $showPartialCorrectAnswers = 1;
   35 
   36 $a = non_zero_random(-9,9,1);
   37 $b = non_zero_random(-9,9,1);
   38 if ($b == $a) { $b = 10; }
   39 
   40 $k = random(2,9,1)*random(-1,1,2);
   41 
   42 $ans1 = $k*$a;
   43 $ans2 = $k*$b;
   44 $ans3 = $a;
   45 $ans4 = - $b;
   46 $ans5 = $a/($a*$a + $b*$b);
   47 $ans6 = - $b/($a*$a + $b*$b);
   48 
   49 BEGIN_TEXT
   50 
   51 Let \( z = $a + $b i\). Write the following numbers in \(a+bi\) form:
   52 $PAR
   53 (a) \($k z = \) \{ans_rule(10)\} \(+\) \{ans_rule(10)\} \(i\),
   54 $PAR
   55 (b) \(\bar{z} = \) \{ans_rule(10)\} \(+\) \{ans_rule(10)\} \(i\),
   56 $PAR
   57 (c) \( \displaystyle \frac{1}{z} = \) \{ans_rule(10)\} \(+\) \{ans_rule(10)\} \(i\).
   58 
   59 END_TEXT
   60 
   61 ANS(num_cmp($ans1));
   62 ANS(num_cmp($ans2));
   63 ANS(num_cmp($ans3));
   64 ANS(num_cmp($ans4));
   65 ANS(num_cmp($ans5));
   66 ANS(num_cmp($ans6));
   67 
   68 ENDDOCUMENT();       # This should be the last executable line in the problem.
   69