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Consider a function F=u+iv which is analytic on the set D={z|Rez>1} and that u_x+v_y=0 on D....

Consider a function F=u+iv which is analytic on the set D={z|Rez>1} and that u_x+v_y=0 on D. Show that there exists a real constant p and a complex constant q such that F(z)=-ipz+q on D.

Notation: Here u_x denotes the partial derivative of u with respect to x and v_y denotes the partial derivative of v with respect to y.

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