View of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers/ur_cn_1_21.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('Complex Analysis')
   15 ## EditionText1('3')
   16 ## AuthorText1('Saff, Snider')
   17 ## Section1('1.4')
   18 ## Problem1('')
   19 
   20 
   21 DOCUMENT();        # This should be the first executable line in the problem.
   22 
   23 loadMacros(
   24 "PG.pl",
   25 "PGbasicmacros.pl",
   26 "PGchoicemacros.pl",
   27 "PGanswermacros.pl",
   28 "PGauxiliaryFunctions.pl",
   29 "PGcomplexmacros.pl"
   30 );
   31 
   32 TEXT(beginproblem());
   33 $showPartialCorrectAnswers = 1;
   34 
   35 $d = random(2,4,1);
   36 $e = random(2,4,1);
   37 
   38 BEGIN_TEXT
   39 
   40 Write each of the given numbers in the form \(a+bi\) :$PAR
   41 (a) \( \displaystyle e^{-\frac{i \pi}{$d}}\) $PAR \{ans_rule(10)\} \( + \) \{ans_rule(10)\}\(i\),$PAR
   42 (b) \( \displaystyle \frac{ e^{(1+i$e\pi)}}{e^{(-1+\frac{i\pi}{2})}}\) $PAR \{ans_rule(10)\} \( + \) \{ans_rule(10)\}\(i\),$PAR
   43 (c) \( \displaystyle e^{e^{i}}\) $PAR \{ans_rule(10)\} \( + \) \{ans_rule(10)\}\(i\).$PAR
   44 $PAR
   45 END_TEXT
   46 
   47 $a = new Complex();
   48 $a = exp(-3.14159265358979/$d*i);
   49 $b = new Complex();
   50 $b = (exp(1+3.14159265358979*$e*i))/(exp(-1+3.14159265358979/2*i));
   51 $c = new Complex();
   52 $c = (exp(exp(i)));
   53 
   54 ANS(num_cmp( $a -> Re ));
   55 ANS(num_cmp( $a -> Im ));
   56 ANS(num_cmp( $b -> Re, tol=>.001));
   57 ANS(num_cmp( $b -> Im));
   58 ANS(num_cmp( $c -> Re ));
   59 ANS(num_cmp( $c -> Im ));
   60 
   61 
   62 
   63 ENDDOCUMENT();        # This should be the last executable line in the problem.
   64