## DESCRIPTION ## Calculus ## ENDDESCRIPTION ## KEYWORDS ('complex','imaginary','derivative') ## Tagged by cmd6a 4/20/06 ## DBsubject('Calculus') ## DBchapter('Appendixes') ## DBsection('Complex Analytic Functions') ## Date('') ## Author('') ## Institution('Rochester') ## TitleText1('Complex Analysis') ## EditionText1('') ## AuthorText1('Saff, Snyder') ## Section1('2.3') ## Problem1('7') 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()); $a = random( 1, 6, 1 );$b = random( 3, 6, 1 ); $c = random( 2, 5, 1 );$d = random( 1, 7, 1 ); $f = random( 5, 8, 1 );$g = random( 2, 8, 1 ); $h = random( 1, 5, 1 );$j = random( 3, 7, 1 ); $k = random( 2, 7, 1 ); BEGIN_TEXT Find the derivatives of the following functions:$PAR (1) $$f(z)\ =\ \frac{(z\ +\ a)^b}{(z^2\ +\ c iz\ +\ d)^f}$$\{ans_rule(40)\}$PAR (2) $$f(z)\ =\ g i(z^3\ -\ h)^j(z^2+k iz)^{100}$$\{ans_rule(40)\}$PAR $PAR END_TEXT$ans = "(z+$a)**($b-1)*($b*(z**2+$c*i*z+$d)-$f*(z+$a)*(2*z+$c*i))/(z**2+$c*i*z+$d)**($f+1)"; ANS(fun_cmp($ans, var => [ 'z', 'i' ])); $ans = "$g*i*(z**3-$h)**($j-1)*(z**2+$k*i*z)**99*($j*(3*z**2)*(z**2+$k*i*z)+100*(2*z+$k*i)*(z**3-$h))"; ANS(fun_cmp($ans, var => [ 'z', 'i' ])); ENDDOCUMENT(); # This should be the last executable line in the problem.