$5-26.$ In the RL circuit shown in Fig. P$5\mathrm{.}26,$ the impedances of $R$ and $L$ are given as $Z_R=R$ and $Z_C=j{x}_L,$ where $j=\sqrt[\phantom{2}]{-1}.$ Suppose $R=100$ and $x_L=50.$

$($a$)$ Express the impedances $Z_R$ and $Z_L$ as complex numbers in both rectangular and polar forms.

$($b$)$ Find the total impedance $Z=Z_R+Z_L$ as a complex number in both rectangular and polar forms.

$($c$)$ If $V=\frac{100}{{?}_0}V,$ find the current $I=\frac{V}{Z}$ as a complex number in both rectangular and polar forms.

$($d$)$ Knowing the current in part $($c$),$ find the voltage phasors $V_R=I{Z}_R$ and $V_L=I{Z}_L$ in both rectangular and polar forms.

$($e$)$ Show that the KVL is satisfied for the circuit shown in Fig. P$5\mathrm{.}26$; in other words, show $V=V_R+V_L.$