$($c$)$ A particular $15$ mH Inductor is found to be modelled by the equivalent circuit shown in Figure $2\mathrm{.}2$ when connected to an a$.$c$.$ voltage source. Assuming the a$.$c$.$ voltage source is sinusoidally oscillating at $100$ kHz $,$ calculate the impedance of the real inductor, $\backslash ($ Z$\_\{$T$\}\backslash ),$ at the $\backslash (\{\}^\{-1\}\backslash )$

$[18$ marks$]$

Note: All complex impedances must be given in the form $\backslash (\backslash$boldsymbol$\{$a$\}+\backslash$boldsymbol$\{$j$\}\backslash$boldsymbol$\{$b$\}\backslash ),$ where $\backslash (\backslash$boldsymbol$\{$a$\},\backslash$boldsymbol$\{$b$\}\backslash )$ are real numbers, and $\backslash ($ j$=$v$(-1)\backslash ).$