Let F be a smooth vector field on a simply connected open subset U CR. Show that F is both irrotational and incompressible if and only if it can be written as F = Vf for a smooth function f: U →R satisfying V²ƒ = 0, where V² is the Laplacian operator. Note that a function f that is a solution of the equation V? f = 0 is called a harmonic function.

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