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| 1 : | jj | 61 | ## DESCRIPTION |
| 2 : | jjholt | 473 | ## Algebra of Complex Numbers |
| 3 : | jj | 61 | ## ENDDESCRIPTION |
| 4 : | |||
| 5 : | jjholt | 473 | ## KEYWORDS('complex', 'imaginary') |
| 6 : | jj | 61 | ## Tagged by YL |
| 7 : | |||
| 8 : | ## DBsubject('Calculus') | ||
| 9 : | jjholt | 483 | ## DBchapter('Complex Variables') |
| 10 : | jjholt | 473 | ## DBsection('Complex Numbers') |
| 11 : | jj | 61 | ## Date('') |
| 12 : | ## Author('') | ||
| 13 : | ## Institution('ASU') | ||
| 14 : | jjholt | 480 | ## TitleText1('Calculus: Early Transcendentals') |
| 15 : | ## EditionText1('5') | ||
| 16 : | jj | 61 | ## AuthorText1('Stewart') |
| 17 : | jjholt | 473 | ## Section1('G') |
| 18 : | jj | 61 | ## Problem1('') |
| 19 : | |||
| 20 : | jjholt | 481 | ## TitleText2('Calculus: Early Transcendentals') |
| 21 : | ## EditionText2('6') | ||
| 22 : | ## AuthorText2('Stewart') | ||
| 23 : | ## Section2('G') | ||
| 24 : | ## Problem2('') | ||
| 25 : | |||
| 26 : | jj | 61 | DOCUMENT(); # This should be the first executable line in the problem. |
| 27 : | |||
| 28 : | loadMacros( | ||
| 29 : | "PG.pl", | ||
| 30 : | "PGbasicmacros.pl", | ||
| 31 : | "PGchoicemacros.pl", | ||
| 32 : | "PGanswermacros.pl", | ||
| 33 : | "PGauxiliaryFunctions.pl", | ||
| 34 : | "PGcomplexmacros.pl" | ||
| 35 : | ); | ||
| 36 : | |||
| 37 : | gage | 268 | TEXT(beginproblem()); |
| 38 : | jj | 61 | $showPartialCorrectAnswers = 1; |
| 39 : | |||
| 40 : | $x1 = non_zero_random(-4,4,1); | ||
| 41 : | $y1 = non_zero_random(-4,4,1); | ||
| 42 : | $x2 = non_zero_random(-4,4,1); | ||
| 43 : | $y2 = non_zero_random(-4,4,1); | ||
| 44 : | $c = non_zero_random(-6,6); | ||
| 45 : | |||
| 46 : | $b = ($x1*$x2*$c+$y1*$y2*$c)/($x2**2+$y2**2); | ||
| 47 : | $a = (-$x1*$y2*$c+$x2*$y1*$c)/($x2**2+$y2**2); | ||
| 48 : | |||
| 49 : | BEGIN_TEXT; | ||
| 50 : | Evaluate the expression | ||
| 51 : | \[ \frac{($x1 - $y1 i)($c i)}{$x2 - $y2 i}\] | ||
| 52 : | and write the result in the form \(a+ b i\). | ||
| 53 : | $BR | ||
| 54 : | Then \(a = \) \{ans_rule(10)\} and \(b = \) \{ans_rule(10)\} | ||
| 55 : | |||
| 56 : | END_TEXT | ||
| 57 : | |||
| 58 : | |||
| 59 : | |||
| 60 : | ANS(num_cmp($a)); | ||
| 61 : | ANS(num_cmp($b)); | ||
| 62 : | |||
| 63 : | |||
| 64 : | ENDDOCUMENT(); # This should be the last executable line in the problem. | ||
| 65 : |
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