Complex Algebra and Analysis (1) Show that the function f(z) =z z, where z-r + jy, is not analytic anywhere in the complex plane. (2) It is given that dz -42-3 and f(2=1+3)--33. Find f(z) from the above information and the harmonic functions u(r, y) and v(x, y) such that f (z) =u(x, y) + JU(x, y). (3) Lit u(r, y)=ry-r+y. Show that u(r, y) is a harmonic function and find its complex conjugate function v(r, y)