How do I check if a force field is potential?

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danilo_rj
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I've got a problem from Irodov.
There are two stationary fields of force F=ayi and F = axi + byj, where i and j are unit vectors of the x and y axes, and a and b are constants. Find out whether these fields are potential.
But how do I know that a field is potential? I've read that I have to calculate the work performed by these forces and if the work depends on the path or not. But why of this?
 
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I think Checking whether the curl of total fields is zero or not is the best way