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The question for the following circuit was to find the average power through the load \$ Z_{L} \$.

The first and second image shows that \$ I_{2} \$ and \$ V_{2} \$ were found. I assumed that the average power through the load could be then found by the formula:

$$ I_{2(rms)}*V_{2(rms)} * cos(18.43 + 45) $$

Exam question (1)

Exam question (2)

However, this appears to yield a different answer to that obtained in the image, where the average power is found directly via the resistor and \$ P = 62.51W \$ is obtained:

Exam question (3)

Could someone please explain why this is the case?

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Embarrassingly I found out that my error was a small and stupid calculation mistake that I was consistently making while inputting my values into a calculator. Both methods do yield the same answer.

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