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Fri Apr 28 13:46:21 2006 UTC (7 years ago) by jjholt
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Added tags.  --JH


    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
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
27 "PGauxiliaryFunctions.pl",
28 "PGcomplexmacros.pl"
29 );
30
31 TEXT(beginproblem());
32 $showPartialCorrectAnswers = 1; 33 34$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