7.19. Suppose that u is harmonic in a domain S. Show that: (a). If v is a harmonic conjugate of u, then -u is a harmonic conjugate of v. (b). If vi and v2 are harmonic conjugates of u, then vi and v2...

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Extracted text: 7.19. Suppose that u is harmonic in a domain S. Show that: (a). If v is a harmonic conjugate of u, then -u is a harmonic conjugate of v. (b). If vi and v2 are harmonic conjugates of u, then vi and v2 differ by a real constant. (c). If v is a harmonic conjugate of u, then v is also a harmonic conjugate of u + c, where c is any real constant.