a. Let f(z) = z + 1/z. Determine all points at which f(z) is analytic. Use the Cauchy-Riemann equations to determine f'(z).
b. Let v = (x^2 - y^2)^2. Determine if v is harmonic. If your answer is yes, find a corresponding analytic function f(z) = u(x,y) + iv(x,y).
c. Let f(z) = e^(-x)e^(-iy). Show that f(z) is analytic everywhere and determine its derivative.
Please help!! And if you could show the steps so I could follow what you are doing, I would really appreciate it.