[npl] / trunk / NationalProblemLibrary / Utah / Intermediate_Algebra / set8_Quadratic_Equations_Functions_and_Inequalities / s8p12.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

Sat Feb 7 16:55:50 2009 UTC (4 years, 3 months ago) by jj
File size: 1411 byte(s)
Fixed NPL tags.


    1 ##DESCRIPTION
2 ##Arithmetic
3 ##ENDDESCRIPTION
4 ## Author('Utah ww group')
5 ## Institution('Univeristy of Utah')
6 ## DBsubject('Algebra')
7 ## DBchapter('Equations and Inequalities')
8 ## DBsection('Complex Numbers')
9 ## AuthorText1('Ron Larson and Robert P. Hostetler')
10 ## TitleText1('Intermediate Algebra')
11 ## EditionText1('4')
12 ## Section1(' Radicals and Complex Numbers ')
13 ## Problem1('')
14
15 ##KEYWORDS('algebra')
16
17 DOCUMENT();        # This should be the first executable line in the problem.
18
20 "PG.pl",
21 "PGbasicmacros.pl",
22 "PGchoicemacros.pl",
24 "PGauxiliaryFunctions.pl"
25 );
26
27 TEXT(&beginproblem);
28
29 TEXT(EV2(<<EOT));
31
32 $BR 33 $$\frac{1}{a+b i}=$$ \{ ans_rule(20) \} $$+$$ 34 EOT 35 &ANS(multivar_function_cmp("a/(a**2+b**2)",["a","b"],[[1,10],[1,10]])); 36 TEXT(EV2(<<EOT)); 37 \{ ans_rule(20) \} $$i$$ 38 EOT 39 &ANS(multivar_function_cmp("-b/(a**2+b**2)",["a","b"],[[1,10],[1,10]])); 40 41 42 TEXT(EV3(<<'EOT')); 43$BR Hint:  This is just a special case of one of the formulas entered earlier.
44 EOT
45
46 SOLUTION(EV3(<<'EOT'));
47 $BR$BBOLD Solution:\$EBOLD  We just multiply with the conjugate complex of the denominator in numerator and denominator:
48 $\frac{a}{a+bi} = \frac{a-bi}{(a+bi)(a-bi)}= \frac{a-bi}{a^2+b^2} = 49 \frac{a}{a^2+b^2} -\frac{b}{a^2+b^2}i.$
50 EOT
51
52
53 ENDDOCUMENT();        # This should be the last executable line in the problem.