View of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers/ur_cn_1_13.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('Appendixes')
   10 ## DBsection('Complex Numbers')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('Complex Analysis')
   15 ## EditionText1('')
   16 ## AuthorText1('Saff, Snyder')
   17 ## Section1('1.3')
   18 ## Problem1('16')
   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 # create random variables
   35 $a = non_zero_random( 2, 3, 1 );
   36 $b = non_zero_random( 20, 100, 1 );
   37 $c = non_zero_random( -100, -20, 1);
   38 
   39 BEGIN_TEXT
   40 Calculate the following:$PAR
   41 (a) \(i^$a\ =\) \{ans_rule(5)\}, $PAR
   42 (b) \(i^\{$a+1\}\ =\) \{ans_rule(5)\}, $PAR
   43 (c) \(i^\{$a+2\}\ =\) \{ans_rule(5)\}, $PAR
   44 (d) \(i^\{$a+3\}\ =\) \{ans_rule(5)\}, $PAR
   45 (e) \(i^{$b}\ =\) \{ans_rule(5)\},$PAR
   46 (f) \(i^{0}\ =\) \{ans_rule(5)\},$PAR
   47 (g) \(i^{-1}\ =\) \{ans_rule(5)\},$PAR
   48 (h) \(i^{-2}\ =\) \{ans_rule(5)\},$PAR
   49 (i) \(i^{-3}\ =\) \{ans_rule(5)\},$PAR
   50 (j) \(i^{$c}\ =\) \{ans_rule(5)\}.$PAR
   51 END_TEXT
   52 
   53 ANS(cplx_cmp( (new Complex( 0, 1) )**$a ) );
   54 ANS(cplx_cmp( (new Complex( 0, 1) )**($a+1) ) );
   55 ANS(cplx_cmp( (new Complex( 0, 1) )**($a+2) ) );
   56 ANS(cplx_cmp( (new Complex( 0, 1) )**($a+3) ) );
   57 ANS(cplx_cmp( (new Complex( 0, 1) )**$b ) );
   58 ANS(cplx_cmp( (new Complex( 0, 1) )**0 ) );
   59 ANS(cplx_cmp( (new Complex( 0, 1) )**(-1) ) );
   60 ANS(cplx_cmp( (new Complex( 0, 1) )**(-2) ) );
   61 ANS(cplx_cmp( (new Complex( 0, 1) )**(-3) ) );
   62 ANS(cplx_cmp( (new Complex( 0, 1) )**$c ) );
   63 
   64 ENDDOCUMENT();        # This should be the last executable line in the problem.
   65