Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN: 9781133382119
Author: Swokowski
Publisher: Cengage
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Question
1.19. 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 v and v₂ are harmonic conjugates of u, then 1 and 2 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.
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Transcribed Image Text:1.19. 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 v and v₂ are harmonic conjugates of u, then 1 and 2 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.
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