## DESCRIPTION
## Imaginary Roots of Quadratics
## ENDDESCRIPTION

## KEYWORDS('complex', 'imaginary', 'quadratic', 'root')
## Tagged by YL

## DBsubject('Calculus')
## DBchapter('Appendixes')
## DBsection('Complex Numbers')
## Date('')
## Author('')
## Institution('ASU')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('G')
## Problem1('')

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

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

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

$b =  random(1,4,1);
$c =  random(5,8,1);

TEXT(EV2(<<EOT));
Find all solutions of the equation \( x+$b+\frac{$c}{x} = 0\) and
express them in the form \(a + b i\):
$BR $BR 
First input the solution with \(b <0\) here:
$BR

 \{ans_rule(25) \}
$BR
Then input the solution with \(b > 0\) here:
$BR

 \{ans_rule(25) \}
$BR
EOT

$nb=-$b;
$delta=-$b**2+4*$c;
$ans1 = $nb/2;
$ans2 = ($delta)**0.5/2; 
$ans3 = $nb/2;
$ans4 = ($delta)**0.5/2; 

ANS(number_list_cmp("$ans1-$ans2*i",complex=>'ok'));

ANS(number_list_cmp("$ans3+$ans4*i",complex=>'ok'));


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