Problem #$3$: Power Factor Correction

A washing machine connected to a household outlet can be modeled as the circuit below:

Where $v(t)=170cos(120t)V$ and $i(t)=4cos(120t-40)A.$ Determine the following:

a$)$ Complex Power.

b$)$ Real Power.

c$)$ Reactive Power.

d$)$ Power factor and whether it is lagging or leading.

e$)$ The impedance $Z_L$ in polar and Cartesian form.

f$)$ The values of the resistors, capacitors and$/$or inductors needed to realize $Z_L.$

g$)$ The capacitor needed in parallel to load $Z_L$ to improve the power factor to $pf=0\mathrm{.}99.$