the current in a circuit is 45+ j12A when the voltage is 82+j100V. determine the phase angle between voltage and current, the power factor, the active power, the reactive power and the apparent power in the circuit

Aheat pump using refrigerant-134a heats a house by using underground water at 8°c as the heat source. the house is losing heat at a rate of 60,000 kj/h. the refrigerant enters the compressor at 280 kpa and 0°c, and it leaves at 1 mpa and 60°c. the refrigerant exits the condenser at 30°c. determine: (a) the power input to the heat pump, (b) the rate of heat absorption from the water, and (c) the increase in electric power input if an electric resistance heater is used instead of a heat pump