View of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers/ur_cn_1_14.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 ## NOTE: answers should implement strict mode once available in cplx_cmp
   21 
   22 DOCUMENT();        # This should be the first executable line in the problem.
   23 
   24 loadMacros(
   25 "PG.pl",
   26 "PGbasicmacros.pl",
   27 "PGchoicemacros.pl",
   28 "PGanswermacros.pl",
   29 "PGauxiliaryFunctions.pl",
   30 "PGcomplexmacros.pl"
   31 );
   32 
   33 TEXT(beginproblem());
   34 $showPartialCorrectAnswers = 1;
   35 
   36 # create random variables
   37 $a = new Complex( non_zero_random( -5, 5, 1 ), non_zero_random( -5, 5, 1));
   38 $b = non_zero_random( -5, 5, 1 );
   39 $c = non_zero_random( 0, 5, 1 );
   40 
   41 
   42 BEGIN_TEXT
   43 
   44 Let \( z\ =\ $a\). Calculate the following:$PAR
   45 (a) \(z^2\ +\ 2z+ 1\ =\) \{ans_rule(10)\} \(+\) \{ans_rule(10)\} \(i\), $PAR
   46 (b) \(z^2\ +\ iz\ -\ ($b\ +\ i)\ =\) \{ans_rule(10)\} \(+\) \{ans_rule(10)\} \(i\), $PAR
   47 (c) \( \displaystyle \frac{(z\ -\ $c)^2}{z\ +\ i}\ =\) \{ans_rule(10)\} \(+\) \{ans_rule(10)\} \(i\).
   48 
   49 END_TEXT
   50 
   51 # cplx_cmp does not currently have a strict mode, these questions should
   52 # implement it when it does
   53 ANS(num_cmp(( $a**2 + 2 * $a + 1) -> Re) );
   54 ANS(num_cmp(( $a**2 + 2 * $a + 1) -> Im) );
   55 ANS(num_cmp(( ($a**2 + (new Complex( 0, 1)*$a - ( $b + (new Complex( 0, 1
   56 )))))) -> Re));
   57 ANS(num_cmp(( ($a**2 + (new Complex( 0, 1)*$a - ( $b + (new Complex( 0, 1
   58 )))))) -> Im));
   59 ANS(num_cmp(( ($a - $c)**2 / ( $a + (new Complex( 0, 1) )) ) -> Re ));
   60 ANS(num_cmp(( ($a - $c)**2 / ( $a + (new Complex( 0, 1) )) ) -> Im ));
   61 ENDDOCUMENT();        # This should be the last executable line in the problem.
   62