Question: Let the function f (z) = u(x, y) + iv(x, y) be analytic in some domain D. State why the functions U(x, y) = eu(x,y)

Let the function f (z) = u(x, y) + iv(x, y) be analytic in some domain D. State why the functions
U(x, y) = eu(x,y) cos v(x, y), V (x, y) = eu(x,y) sin v(x, y)
are harmonic in D and why V (x, y) is, in fact, a harmonic conjugate of U(x, y).

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