Show that (1 ) arctan (y x) is harmonic in the upper half plane and satisfies the boundary condition (x, 0) 1 if x 0 and 0 if x 0, and the corresponding complex potential is F(z) (i ) Ln Z

Question: Show that = / = (1/) arctan (y/x) is harmonic in the upper half-plane and satisfies the boundary condition (x, 0) = 1

Show that Φ = θ/π = (1/π) arctan (y/x) is harmonic in the upper half-plane and satisfies the boundary condition Φ (x, 0) = 1 if x < 0 and 0 if x > 0, and the corresponding complex potential is F(z) = -(i/π) Ln Z.

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