## 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('Fundamentals of Complex Analysis for Mathematics, Science, and Engineering')
## EditionText1('')
## AuthorText1('E.B. Saff and A.D. Snider')
## 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.