A particle in the \(xy\)-plane is acted upon by a force field described by the equation below: \[\large{\vec{F} = x \hat{\imath} + y \hat{\jmath}}.\] How much work does the force field do on the particle if the particle makes one complete revolution over a unit circle centered on the origin?

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**Notes:**

- \(\hat{\imath}\) and \(\hat{\jmath}\) denote unit vectors in the \(x\) and \(y\) directions, respectively.
- Give your answer to 3 decimal places.

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