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| 1 : | jj | 517 | ##DESCRIPTION |
| 2 : | ## Algebra problem: complex numbers | ||
| 3 : | ##ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | ##KEYWORDS('algebra', 'quadratic equation') | ||
| 6 : | |||
| 7 : | ## tcao , PAID on 11-24-2003 | ||
| 8 : | |||
| 9 : | ## DBsubject('Algebra') | ||
| 10 : | ## DBchapter('Polynomial and Rational Functions') | ||
| 11 : | ## DBsection('Complex Roots/Fundamental Theorem of Algebra') | ||
| 12 : | ## Date('6/3/2002') | ||
| 13 : | ## Author('') | ||
| 14 : | ## Institution('') | ||
| 15 : | ## TitleText1('Precalculus') | ||
| 16 : | ## EditionText1('3') | ||
| 17 : | ## AuthorText1('Stewart, Redlin, Watson') | ||
| 18 : | ## Section1('3.4') | ||
| 19 : | ## Problem1('11') | ||
| 20 : | 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 : | ); | ||
| 29 : | |||
| 30 : | TEXT(beginproblem()); | ||
| 31 : | $showPartialCorrectAnswers = 1; | ||
| 32 : | |||
| 33 : | $b = random(2,4,1); | ||
| 34 : | $c = random(5,8,1); | ||
| 35 : | |||
| 36 : | TEXT(EV2(<<EOT)); | ||
| 37 : | Find all solutions of the equation \( t + $b + \frac{$c}{t} = 0\) and | ||
| 38 : | express them in the form \(a + b i\): | ||
| 39 : | $BR $BR | ||
| 40 : | First input the solution with \(b <0\) here: | ||
| 41 : | $BR | ||
| 42 : | the real part \(a\) equals \{ans_rule(20) \} | ||
| 43 : | and the imaginary part \( b \) equals \{ans_rule(20) \} | ||
| 44 : | $BR | ||
| 45 : | Then input the solution with \(b > 0\) here: | ||
| 46 : | $BR | ||
| 47 : | the real part \(a\) equals \{ans_rule(20) \} | ||
| 48 : | and the imaginary part \( b \) equals \{ans_rule(20) \} | ||
| 49 : | $BR | ||
| 50 : | EOT | ||
| 51 : | |||
| 52 : | $ans1 = -$b/2; | ||
| 53 : | $ans2 = -(-$b**2+4*$c)**(1/2)/2; | ||
| 54 : | $ans3 = -$b/2; | ||
| 55 : | $ans4 = (-$b**2+4*$c)**(1/2)/2; | ||
| 56 : | |||
| 57 : | ANS(num_cmp($ans1)); | ||
| 58 : | ANS(num_cmp($ans2)); | ||
| 59 : | ANS(num_cmp($ans3)); | ||
| 60 : | ANS(num_cmp($ans4)); | ||
| 61 : | |||
| 62 : | ENDDOCUMENT(); # This should be the last executable line in the problem. | ||
| 63 : |
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