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

Tue Jun 26 21:45:47 2007 UTC (5 years, 11 months ago) by jjholt
File size: 1776 byte(s)
```Updated tags. --JJH
```

```    1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS ('complex','imaginary')
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('Complex Analysis')
15 ## EditionText1('')
16 ## AuthorText1('Saff, Snyder')
17 ## Section1('1.3')
18 ## Problem1('16')
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 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 ) );
54 ANS(cplx_cmp( (new Complex( 0, 1) )**(\$a+1) ) );
55 ANS(cplx_cmp( (new Complex( 0, 1) )**(\$a+2) ) );
56 ANS(cplx_cmp( (new Complex( 0, 1) )**(\$a+3) ) );
57 ANS(cplx_cmp( (new Complex( 0, 1) )**\$b ) );
58 ANS(cplx_cmp( (new Complex( 0, 1) )**0 ) );
59 ANS(cplx_cmp( (new Complex( 0, 1) )**(-1) ) );
60 ANS(cplx_cmp( (new Complex( 0, 1) )**(-2) ) );
61 ANS(cplx_cmp( (new Complex( 0, 1) )**(-3) ) );
62 ANS(cplx_cmp( (new Complex( 0, 1) )**\$c ) );
63
64 ENDDOCUMENT();        # This should be the last executable line in the problem.
65
```

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