Resistor Heat Dissipation (with imaginary numbers)

[derek88]

Friends:

I am wondering about heat dissipation when you have imaginary numbers.

Lets say a current I = (3 + 4j) Amps is going through an impedance Z = (2 + 3j) Ohms. What is the amount of heat dissipated by the impedance?

I think that you take the magnitude of the current, |I| = 5 Amps, and then find the heat dissipated by only the real part of the impedance, Re(Z) = 2. The heat dissipated would be P = (5^2)*2 = 50 W.

Is this correct?

Note: This is not a homework question. This is something I just wanted to verify.

 

[I like Serena]

The RMS power is:
$$P_{RMS}={|I|^2 \over 2} |Z|$$