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Solution If uand vare harmonic, then is harmonic since ∂2(uv) ∂x 2 ∂2(uv) ∂y2 = ∂2u ∂x ∂2v ∂x2 ∂2u ∂y2 ∂2v ∂y = ∂2u ∂x 2 ∂ 2u ∂y2 ∂2v ∂x ∂ v ∂y2 = 0 To show that uv is not necessarily harmonic, it s.

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