View of /trunk/NationalProblemLibrary/Rochester/setAlgebra11ComplexNumbers/beth1complex.pg

    1 ## DESCRIPTION
    2 ##   Complex Numbers
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Complex', 'Imaginary')
    6 ## Tagged by nhamblet
    7 
    8 ## DBsubject('Algebra')
    9 ## DBchapter('Equations and Inequalities')
   10 ## DBsection('Complex Numbers')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl",
   28 "PGcomplexmacros.pl"
   29 );
   30 
   31 TEXT(beginproblem());
   32 $showPartialCorrectAnswers = 1;
   33 
   34 $x1 = non_zero_random(-4,4,1);
   35 $y1 = non_zero_random(-4,4,1);
   36 $x2 = non_zero_random(-4,4,1);
   37 $y2 = non_zero_random(-4,4,1);
   38 $c = non_zero_random(-6,6);
   39 
   40 $b = ($x1*$x2*$c+$y1*$y2*$c)/($x2**2+$y2**2);
   41 $a = (-$x1*$y2*$c+$x2*$y1*$c)/($x2**2+$y2**2);
   42 
   43 BEGIN_TEXT;
   44 Evaluate the expression
   45 \[ \frac{($x1 - $y1 i)($c i)}{$x2 - $y2 i}\]
   46 and write the result in the form \(a+ b i\).
   47 $BR
   48 Then \(a = \) \{ans_rule(10)\} and \(b = \) \{ans_rule(10)\}
   49 
   50 END_TEXT
   51 
   52 
   53 
   54 ANS(num_cmp($a));
   55 ANS(num_cmp($b));
   56 
   57 
   58 ENDDOCUMENT();        # This should be the last executable line in the problem.