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# View of /trunk/NationalProblemLibrary/Rochester/setAlgebra11ComplexNumbers/beth1complex.pg

Tue Apr 11 16:55:13 2006 UTC (7 years, 1 month ago) by jjholt
File size: 1199 byte(s)
Added tags.  --JH


    1 ## DESCRIPTION
2 ##   Complex Numbers
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('Complex', 'Imaginary')
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('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
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 $showPartialCorrectAnswers = 1; 33 34$x1 = non_zero_random(-4,4,1);
35 $y1 = non_zero_random(-4,4,1); 36$x2 = non_zero_random(-4,4,1);
37 $y2 = non_zero_random(-4,4,1); 38$c = non_zero_random(-6,6);
39
40 $b = ($x1*$x2*$c+$y1*$y2*$c)/($x2**2+$y2**2); 41$a = (-$x1*$y2*$c+$x2*$y1*$c)/($x2**2+$y2**2);
42
43 BEGIN_TEXT;
44 Evaluate the expression
45 $\frac{(x1 - y1 i)(c i)}{x2 - y2 i}$
46 and write the result in the form $$a+ b i$$.
47 $BR 48 Then $$a =$$ \{ans_rule(10)\} and $$b =$$ \{ans_rule(10)\} 49 50 END_TEXT 51 52 53 54 ANS(num_cmp($a));
55 ANS(num_cmp(\$b));
56
57
58 ENDDOCUMENT();        # This should be the last executable line in the problem.