## DESCRIPTION ## Algebra of Complex Numbers ## ENDDESCRIPTION ## KEYWORDS('complex', 'imaginary') ## Tagged by YL ## DBsubject('Calculus') ## DBchapter('Complex Variables') ## DBsection('Complex Numbers') ## Date('') ## Author('') ## Institution('ASU') ## TitleText1('Calculus: Early Transcendentals') ## EditionText1('5') ## AuthorText1('Stewart') ## Section1('G') ## Problem1('') ## TitleText2('Calculus: Early Transcendentals') ## EditionText2('6') ## AuthorText2('Stewart') ## Section2('G') ## Problem2('') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl", "PGcomplexmacros.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 1;$x1 = non_zero_random(-4,4,1); $y1 = non_zero_random(-4,4,1);$x2 = non_zero_random(-4,4,1); $y2 = non_zero_random(-4,4,1);$c = non_zero_random(-6,6); $b = ($x1*$x2*$c+$y1*$y2*$c)/($x2**2+$y2**2);$a = (-$x1*$y2*$c+$x2*$y1*$c)/($x2**2+$y2**2); BEGIN_TEXT; Evaluate the expression $\frac{(x1 - y1 i)(c i)}{x2 - y2 i}$ and write the result in the form $$a+ b i$$. $BR Then $$a =$$ \{ans_rule(10)\} and $$b =$$ \{ans_rule(10)\} END_TEXT ANS(num_cmp($a)); ANS(num_cmp(\$b)); ENDDOCUMENT(); # This should be the last executable line in the problem.