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# View of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers/ur_cn_1_14.pg

Tue Jul 3 17:27:24 2007 UTC (5 years, 10 months ago) by jjholt
File size: 1792 byte(s)
Updated Tags.  --JJH


    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
25 "PG.pl",
26 "PGbasicmacros.pl",
27 "PGchoicemacros.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