## 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.