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# View of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers/ur_cn_1_13.pg

Fri Apr 16 21:43:48 2010 UTC (3 years, 1 month ago) by jj
File size: 1933 byte(s)
```Fixed bug 1769, problem did not require students to actually do the computations.
```

```    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('Complex Analysis')
15 ## EditionText1('3')
16 ## AuthorText1('Saff, Snider')
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());
33
34 # create random variables
35 \$a = non_zero_random( 2, 3, 1 );
36 \$b = non_zero_random( 20, 100, 1 );
37 \$c = non_zero_random( -100, -20, 1);
38
39 BEGIN_TEXT
40 Calculate the following:\$PAR
41 (a) \(i^\$a\ =\) \{ans_rule(5)\} \$PAR
42 (b) \(i^\{\$a+1\}\ =\) \{ans_rule(5)\} \$PAR
43 (c) \(i^\{\$a+2\}\ =\) \{ans_rule(5)\} \$PAR
44 (d) \(i^\{\$a+3\}\ =\) \{ans_rule(5)\} \$PAR
45 (e) \(i^{\$b}\ =\) \{ans_rule(5)\}\$PAR
46 (f) \(i^{0}\ =\) \{ans_rule(5)\}\$PAR
47 (g) \(i^{-1}\ =\) \{ans_rule(5)\}\$PAR
48 (h) \(i^{-2}\ =\) \{ans_rule(5)\}\$PAR
49 (i) \(i^{-3}\ =\) \{ans_rule(5)\}\$PAR
50 (j) \(i^{\$c}\ =\) \{ans_rule(5)\}.\$PAR
51 END_TEXT
52
53 ANS(cplx_cmp( (new Complex( 0, 1) )**\$a, mode=>'strict' ) );
54 ANS(cplx_cmp( (new Complex( 0, 1) )**(\$a+1), mode=>'strict' ) );
55 ANS(cplx_cmp( (new Complex( 0, 1) )**(\$a+2), mode=>'strict' ) );
56 ANS(cplx_cmp( (new Complex( 0, 1) )**(\$a+3), mode=>'strict' ) );
57 ANS(cplx_cmp( (new Complex( 0, 1) )**\$b, mode=>'strict' ) );
58 ANS(cplx_cmp( (new Complex( 0, 1) )**0, mode=>'strict' ) );
59 ANS(cplx_cmp( (new Complex( 0, 1) )**(-1), mode=>'strict' ) );
60 ANS(cplx_cmp( (new Complex( 0, 1) )**(-2), mode=>'strict' ) );
61 ANS(cplx_cmp( (new Complex( 0, 1) )**(-3), mode=>'strict' ) );
62 ANS(cplx_cmp( (new Complex( 0, 1) )**\$c, mode=>'strict' ) );
63
64 ENDDOCUMENT();        # This should be the last executable line in the problem.
65
```