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.
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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.5: Trigonometric Form For Complex Numbers
Problem 63E
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