## DESCRIPTION ## Complex Numbers ## ENDDESCRIPTION ## KEYWORDS('Complex') ## Tagged by nhamblet ## DBsubject('Algebra') ## DBchapter('Equations and Inequalities') ## DBsection('Complex Numbers') ## Date('') ## Author('') ## Institution('Rochester') ## TitleText1('Complex Analysis') ## EditionText1('3') ## AuthorText1('Saff, Snider') ## Section1('3.1') ## Problem1('') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl", "PGcomplexmacros.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 1; # create four complex numbers$a = new Complex( non_zero_random( -5, 5, 1 ) , non_zero_random( -5, 5, 1 ) ); $b = non_zero_random( 1, 5, 1 );$c = new Complex( non_zero_random( -5, 0, 1 ), non_zero_random( 0, 5, 1 )); BEGIN_TEXT Write the following numbers in $$a\ +\ bi$$ form:$BR (a) $$(a)^2\ =$$ \{ans_rule(5)\} $$+$$ \{ans_rule(5)\} $$i$$,$BR (b) $$i(\pi\ -\ b i)\ =$$ \{ans_rule(5)\} $$+$$ \{ans_rule(5)\} $$i$$,$BR (c) $$\displaystyle \frac{c}{i}\ =$$ \{ans_rule(5)\} $$+$$ \{ans_rule(5)\} $$i$$. END_TEXT ANS(num_cmp( ($a**2) -> Re ) ); ANS(num_cmp( ($a**2) -> Im )); ANS(num_cmp( ($b ))); ANS(num_cmp( $PI )); ANS(num_cmp( ($c -> Im ) )); ANS(num_cmp( -(\$c -> Re ))); ENDDOCUMENT(); # This should be the last executable line in the problem.