View of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers/ur_cn_1_20.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('Appendixes')
   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 "PGauxiliaryFunctions.pl",
   28 "PGcomplexmacros.pl"
   29 );
   30 
   31 TEXT(beginproblem());
   32 $showPartialCorrectAnswers = 1;
   33 
   34 $a = new Complex( 0, $PI );
   35 $b = new Complex( -2*sqrt($one = random(2, 3, 1 )), -($two = non_zero_random( 1, 5, 1 )) );
   36 $c = (new Complex( 1, -1 ) ) * ( new Complex( -sqrt($three=random(2,3,1)), 1 ) );
   37 $d = (new Complex( sqrt($four=random(2,3,1)), ($five = random (-5, -1, 1 )) ) )**2;
   38 $e = ( new Complex( ($six = random(-5, -1, 1 )), sqrt($seven = random(2,3, 1))))/( new Complex(
   39 ($eight = random(1, 5, 1)), ($nine = random( 1, 5, 1 ) )));
   40 $f = -sqrt(7) * ( new Complex( 1, 1 ))/( new Complex( sqrt($ten = random( 2, 3, 1)), 1 ) );
   41 
   42 
   43 BEGIN_TEXT
   44 
   45 Write the following numbers in the polar form \(re^{i \theta} \), \(-\pi < \theta \le \pi\): $PAR
   46 (a) \( \pi i\) $PAR
   47 \( r = \) \{ans_rule(15)\}, \( \theta = \) \{ans_rule(15)\}, $PAR
   48 (b) \( -2\sqrt{$one}\ -\ $two i \) $PAR
   49 \( r = \) \{ans_rule(15)\}, \( \theta = \) \{ans_rule(15)\}, $PAR
   50 (c) \( ( 1\ -\ i)( - \sqrt{$three}\ +\ i)\) $PAR
   51 \( r = \) \{ans_rule(15)\}, \( \theta = \) \{ans_rule(15)\}, $PAR
   52 (d) \((\sqrt{$four}\ $five i)^2\) $PAR
   53 \( r = \) \{ans_rule(15)\}, \( \theta = \) \{ans_rule(15)\}, $PAR
   54 (e) \( \displaystyle \frac{$six\ +\ \sqrt{$seven}i}{$eight\ +\ $nine i}\) $PAR
   55 \( r = \) \{ans_rule(15)\}, \( \theta = \) \{ans_rule(15)\}, $PAR
   56 (f) \( \displaystyle \frac{-\sqrt{7}(1\ +\ i)}{\sqrt{$ten}\ +\ i}\) $PAR
   57 \( r = \) \{ans_rule(15)\}, \( \theta = \) \{ans_rule(15)\}, $PAR
   58 
   59 $PAR $BR
   60 END_TEXT
   61 
   62 
   63 ANS(num_cmp( $a -> rho ));
   64 ANS(num_cmp( $a -> theta));
   65 ANS(num_cmp( $b -> rho ));
   66 ANS(num_cmp( $b -> theta));
   67 ANS(num_cmp( $c -> rho ));
   68 ANS(num_cmp( $c -> theta));
   69 ANS(num_cmp( $d -> rho ));
   70 ANS(num_cmp( $d -> theta));
   71 ANS(num_cmp( $e -> rho ));
   72 ANS(num_cmp( $e -> theta));
   73 ANS(num_cmp( $f -> rho ));
   74 ANS(num_cmp( $f -> theta));
   75 
   76 
   77 
   78 ENDDOCUMENT();        # This should be the last executable line in the problem.
   79