Assignment:
Show that u (x, y) is harmonic in some domain and find a harmonic conjugate v (x, y) when
(a) u (x, y) = 2x (1 - y)
(b) u (x, y) = 2x - x3 + 3xy2
(c) u (x, y) = sinh x·sin y
(d) u (x, y) = y / (x2 + y2)
Provide complete and step by step solution for the question and show calculations and use formulas.