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Let u and v be harmonic functions, and suppose that v is the conjugate of u. Show that eu2-82 cos(2uv) and eu2-82 sin(2uv) are harmonic.

Let u and v be harmonic functions, and suppose that v is the conjugate of u. Show that eu2-82 cos(2uv) and eu2-82 sin(2uv) are harmonic. (Hint: ex is analytic.)

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