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# View of /trunk/NationalProblemLibrary/Rochester/setAlgebra11ComplexNumbers/ur_cn_1_8.pg

Tue Jul 17 13:55:24 2007 UTC (5 years, 10 months ago) by jjholt
File size: 1467 byte(s)
Fixed edition tags.


    1 ## DESCRIPTION
2 ##   Complex Numbers
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('Complex')
6 ## Tagged by nhamblet
7
8 ## DBsubject('Algebra')
9 ## DBchapter('Equations and Inequalities')
10 ## DBsection('Complex Numbers')
11 ## Date('')
12 ## Author('')
13 ## Institution('Rochester')
14 ## TitleText1('Complex Analysis')
15 ## EditionText1('3')
16 ## AuthorText1('Saff, Snyder')
17 ## Section1('1.1')
18 ## Problem1('')
19
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
27 "PGauxiliaryFunctions.pl",
28 "PGcomplexmacros.pl"
29 );
30
31 TEXT(beginproblem());
32 $showPartialCorrectAnswers = 1; 33 34 # create four complex numbers 35$a = new Complex( random(-5,-1,1) , 1 );
36 $c = new Complex( non_zero_random( -5, 5, 1 ) , non_zero_random( -5, 5, 1 ) ); 37$d = non_zero_random( -5, 5, 1 );
38
39 BEGIN_TEXT
40 Write the following numbers in $$a\ +\ bi$$ form:$BR 41 (a) $$(a)^2\ =$$ \{ans_rule(5)\} $$+$$ \{ans_rule(5)\} $$i$$,$BR
42 (b) $$\displaystyle \frac{c}{\frac{i}{d}}\ =$$ \{ans_rule(5)\} $$+$$ \{ans_rule(5)\} $$i$$,$BR 43 (c) $$\displaystyle \frac{c}{\frac{1}{d}}\ =$$ \{ans_rule(5)\} $$+$$ \{ans_rule(5)\} $$i$$.$BR
44
45 END_TEXT
46
47 $b =$c  / ( new Complex( 0, 1/$d )); 48 49 ANS(num_cmp( ($a**2) -> Re ));
50 ANS(num_cmp( ($a**2) -> Im )); 51 ANS(num_cmp($b -> Re ));
52 ANS(num_cmp( $b -> Im )); 53 ANS(num_cmp( ($c*$d) -> Re )); 54 ANS(num_cmp( ($c*\$d) -> Im ));
55
56 ENDDOCUMENT();        # This should be the last executable line in the problem.
57