View of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers/ur_cn_1_16.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('Complex Analysis')
   15 ## EditionText1('3')
   16 ## AuthorText1('Saff, Snider')
   17 ## Section1('1.3')
   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 "PGauxiliaryFunctions.pl",
   28 "PGcomplexmacros.pl"
   29 );
   30 
   31 TEXT(beginproblem());
   32 $showPartialCorrectAnswers = 1;
   33 
   34 $a = new Complex( non_zero_random( 1, 4, 1 ), non_zero_random(1,4,1));
   35 $b = new Complex( non_zero_random( -4, -1, 1 ), non_zero_random( -4, -1,1));
   36 #$c = new Complex( non_zero_random( 1, 4, 1 ), non_zero_random(1,4,1));
   37 $d = new Complex( non_zero_random( 1, 4, 1 ), non_zero_random(-4,-1,1));
   38 $e = new Complex( non_zero_random( 1, 4, 1 ), non_zero_random(-4,-1,1));
   39 $f = new Complex( non_zero_random( 1, 4, 1 ), non_zero_random(1,4,1));
   40 $g = new Complex( non_zero_random( 1, 4, 1 ), non_zero_random(-4,-1,1));
   41 
   42 BEGIN_TEXT
   43 
   44 Calculate:$PAR
   45 (a) \( \displaystyle \Big| \frac{$a}{$b} \Big|\ = \) \{ans_rule(20)\}, $PAR
   46 (b) \( \displaystyle \Big| \overline{(1\ +\ i)}($d)($e)\Big|\ =\) \{ans_rule(20)\}, $PAR
   47 (c) \( \displaystyle \Big|\frac{i($f)^3}{($g)^2}\Big|\ =\) \{ans_rule(20)\}, $PAR
   48 (d) \( \displaystyle \Big| \frac{(\pi\ + i) ^{100}}{(\pi\ -\ i)^{100}}\Big|\ =\) \{ans_rule(20)\}.
   49 
   50 END_TEXT
   51 
   52 $i = new Complex( 0,1);
   53 $pi = 3.14159265359;
   54 
   55 ANS(num_cmp( (($a)/($b) ) -> abs ));
   56 ANS(num_cmp( ((1-$i)*($d)*($e)) -> abs ) );
   57 ANS(num_cmp( ($i*($f)**3 / ($g)**2 ) -> abs ) );
   58 ANS(num_cmp( ((($pi + $i )**100)/(($pi - $i)**100))-> abs ) );
   59 
   60 
   61 ENDDOCUMENT();        # This should be the last executable line in the problem.
   62