Power Consumption (effective power)

Hi, can you please check my answer?
By the way, we don't use calculator at all so we don't have to calculate to the exact value. For example, if there is "pi", we can just leave it as it is, without converting it into 3.142. Also, if there is square root of 2, just leave it as square root of 2, no need to calculate it as 1.41.

Ok, here is the question:
v1(t) and v2(t) are given as written in the question.

1) Find the value of impedance Z.
2) Find the power consumption (effective power) of the entire circuit.

I already got the answer for number 1 but I am confused with no. 2.
I tried to find the effective power in 2 different ways and I got two different answers. Can you explain to me why? I think the answer is 1/2, though.


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