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In the electrotechnics problem, I used the complex number method to find the instantaneous power p of sinusoidal alternating current, and the result was wrong. Why?
Calculate with u(t) * i(t) and get the "instantaneous power".

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Using phasor method, the real part is active power and the imaginary part is reactive power after calculation.

These two are the "average power" in a period.

It is not "instantaneous power".

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Besides, the calculation formula of your phasor method is wrong.

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