## DESCRIPTION
## Complex Arithmetic
## ENDDESCRIPTION

## KEYWORDS('complex numbers', 'multiplication')
## Tagged by tda2d

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

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

## Do NOT show partial correct answers
$showPartialCorrectAnswers = 0;

## Lots of set up goes here
$a = random(-10,10);
$b = random(-10,10);
$c = non_zero_random(-10,10);
$d = non_zero_random(-10,10);


## Ok, we are ready to begin the problem...
##
TEXT(beginproblem());


BEGIN_TEXT
$BR
    Evaluate the expression \(\displaystyle ($a + $b i)($c + $d i)\), and write your answer in the form \( a + b i\).

a = \{ans_rule()\} and b = \{ ans_rule()\}.

$PAR
END_TEXT
    ANS(num_cmp( $a*$c - $b*$d  ));
ANS(num_cmp( $b*$c + $a*$d   ));
ENDDOCUMENT();