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# View of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers/ur_cn_1_36.pg

Tue Jul 3 17:27:24 2007 UTC (5 years, 11 months ago) by jjholt
File size: 1399 byte(s)
Updated Tags.  --JJH

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('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 DOCUMENT();        # This should be the first executable line in the problem.
21
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
27 "PGgraphmacros.pl",
28 "PGmatrixmacros.pl",
29 "PGnumericalmacros.pl",
30 "PGauxiliaryFunctions.pl"
31 );
32
33 TEXT(beginproblem());
34 $showPartialCorrectAnswers = 1; 35 36$r = random(2,9,1);
37 $phi = random(.1,3,.1); 38 39$c = random(2,9,1);
40
41 BEGIN_TEXT
42
43 Let $$z = r (\cos phi + i \sin phi )$$.
44 $PAR 45 Write the following numbers in the polar form $$r(\cos\phi + i \sin \phi)$$, $$0 \le \phi < 2\pi$$. 46$PAR
47 (a) $$c z$$
48 $PAR 49 $$r=$$ \{ans_rule(10)\}, $$\phi=$$ \{ans_rule(10)\}, 50$PAR
51 (b) $$\bar{z}$$
52 $PAR 53 $$r=$$ \{ans_rule(10)\}, $$\phi=$$ \{ans_rule(10)\}, 54$PAR
55 (c) $$\displaystyle \frac{1}{z}$$
56 $PAR 57 $$r=$$ \{ans_rule(10)\}, $$\phi=$$ \{ans_rule(10)\}. 58 59 END_TEXT 60 61 ANS(num_cmp($c*$r)); 62 ANS(num_cmp($phi));
63
64 ANS(num_cmp($r)); 65 ANS(num_cmp(2*$PI - $phi)); 66 67 ANS(num_cmp(1/$r));
68 ANS(num_cmp(2*$PI -$phi));
69
70
71 ENDDOCUMENT();       # This should be the last executable line in the problem.
72