$5-18.$ A series$-$parallel electric circuit consists of the components shown in Fig. P$5\mathrm{.}18.$ The values of the impedance of the two components are $Z_1=\frac{-j}{C}$ and $Z_2=R+jL,$ where $C=5F,R^{}=100,L=0\mathrm{.}15H,=120ra\frac{d}{s},$ and $j=\sqrt[\phantom{2}]{-1}.$

$($a$)$ Write $Z_1$ and $Z_2$ as complex numbers in both their rectangular and polar forms.

$($b$)$ Write down the complex conjugate of $Z_2$ and calculate the product $Z_2{Z}_2^{**}.$

$($c$)$ Calculate the total impedance $Z=\frac{Z_1{Z}_2}{Z_1+Z_2}$ of the circuit. Write the total impedance in both its rectangular and polar forms.