## DESCRIPTION
##   Complex Numbers
## ENDDESCRIPTION

## KEYWORDS('Complex', 'Imaginary')
## Tagged by nhamblet

## DBsubject('Algebra')
## DBchapter('Equations and Inequalities')
## DBsection('Complex Numbers')
## Date('')
## Author('')
## Institution('Rochester')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

$x1 = non_zero_random(-8,8,1);
$y1 = non_zero_random(-8,8,1);
$x2 = non_zero_random(-8,8,1);
$y2 = non_zero_random(-8,8,1);

$a = $x1-$x2;
$b = $y1-$y2;

TEXT(EV2(<<EOT));
Evaluate the expression \( ($x1 ? {$y1} i)-($x2 ? {$y2} i)\) and
write the result in the form \(a+ b i\). 
$BR $BR 
The real number \(a\) equals \{ans_rule(15) \}
$BR
The real number \( b \) equals \{ans_rule(15) \}
$BR
EOT

$ans1 = $a;
$ans2 = $b;
ANS(num_cmp($ans1));
ANS(num_cmp($ans2));

ENDDOCUMENT();        # This should be the last executable line in the problem.