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| 1 : | jjholt | 184 | ## DESCRIPTION |
| 2 : | ## Calculus | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | jj | 143 | |
| 5 : | jjholt | 184 | ## KEYWORDS ('complex','imaginary') |
| 6 : | ## Tagged by cmd6a 4/20/06 | ||
| 7 : | jj | 143 | |
| 8 : | jjholt | 184 | ## DBsubject('Calculus') |
| 9 : | jjholt | 449 | ## DBchapter('Complex Variables') |
| 10 : | jjholt | 184 | ## DBsection('Complex Numbers') |
| 11 : | ## Date('') | ||
| 12 : | ## Author('') | ||
| 13 : | ## Institution('Rochester') | ||
| 14 : | jjholt | 443 | ## TitleText1('Complex Analysis') |
| 15 : | jjholt | 184 | ## EditionText1('') |
| 16 : | jjholt | 443 | ## AuthorText1('Saff, Snyder') |
| 17 : | jjholt | 184 | ## Section1('1.3') |
| 18 : | ## Problem1('16') | ||
| 19 : | |||
| 20 : | jj | 143 | DOCUMENT(); # This should be the first executable line in the problem. |
| 21 : | |||
| 22 : | loadMacros( | ||
| 23 : | "PG.pl", | ||
| 24 : | "PGbasicmacros.pl", | ||
| 25 : | "PGchoicemacros.pl", | ||
| 26 : | "PGanswermacros.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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