## Resistor Heat Dissipation (with imaginary numbers)

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.

 PhysOrg.com physics news on PhysOrg.com >> Iron-platinum alloys could be new-generation hard drives>> Lab sets a new record for creating heralded photons>> Breakthrough calls time on bootleg booze
 Recognitions: Homework Help The RMS power is: $$P_{RMS}={|I|^2 \over 2} |Z|$$

 Tags dissipation, heat, imaginary, impedance, resistance
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