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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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