View of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers/ur_cn_1_36.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS ('complex','imaginary','polar coordinates')
    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 $r = random(2,9,1);
   37 $phi = random(.1,3,.1);
   38 
   39 $c = random(2,9,1);
   40 
   41 BEGIN_TEXT
   42 
   43 Let \(z = $r (\cos $phi + i \sin $phi ) \).
   44 $PAR
   45 Write the following numbers in the polar form \( r(\cos\phi + i \sin \phi)\), \( 0 \le \phi < 2\pi\).
   46 $PAR
   47 (a) \($c z\)
   48 $PAR
   49 \(r=\) \{ans_rule(10)\}, \(\phi=\) \{ans_rule(10)\},
   50 $PAR
   51 (b) \( \bar{z} \)
   52 $PAR
   53 \(r=\) \{ans_rule(10)\}, \(\phi=\) \{ans_rule(10)\},
   54 $PAR
   55 (c) \( \displaystyle \frac{1}{z} \)
   56 $PAR
   57 \(r=\) \{ans_rule(10)\}, \(\phi=\) \{ans_rule(10)\}.
   58 
   59 END_TEXT
   60 
   61 ANS(num_cmp($c*$r));
   62 ANS(num_cmp($phi));
   63 
   64 ANS(num_cmp($r));
   65 ANS(num_cmp(2*$PI - $phi));
   66 
   67 ANS(num_cmp(1/$r));
   68 ANS(num_cmp(2*$PI - $phi));
   69 
   70 
   71 ENDDOCUMENT();       # This should be the last executable line in the problem.
   72