The components in this network have values R$1=1\mathrm{.}6$k$,$ R$2=2\mathrm{.}1$k$,$ and C$=14$F$.$

$($a$)$ Determine the real and imaginary parts of the network's impedance Z $($in $),$ as functions of the angular frequency $($in rad$/$s$).$ Use omega as the variable name.

Re$\{$Z$\}=$

Im$\{$Z$\}=$

$($b$)$ At what value of angular frequency $$ does Im$\{$Z$\}$ reach its maximum magnitude?

rad$/$s

$($c$)$ What is the value of Z at this special frequency?

Re$\{$Z$\}=$

Im$\{$Z$\}=$