b) Let z=x+iy and f be an analytic function on D such that f(x,y)=u(x,y)+iv(x,y), where u,v are real functions. Let (z)=21f(z)2. Show that (i) x=Re(f(z)fx(z))y=Im(f(z)fx(z))wherefx(z)=ux+ivx. (ii). If f(z) is constant in D then f is a constant function (Hint: Use part 1.(b).(i)). c) Determine which of the following functions are entire and which are not. Justify your answer. (i). f(z)=1+z21 (ii). g(z)=3(x2y2)+i6xy