# Math Help - analytic, harmonic, Cauchy-Riemann...

1. ## analytic, harmonic, Cauchy-Riemann...

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.

2. Originally Posted by SoBeautiful
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).
Here.

3. Originally Posted by SoBeautiful

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).
For some reason I think I made a mistake.
This is Mine 57th Post!!!

4. Most importantly about #2, the function v(xy) is not harmonic.

5. What is the E in part b? And doesnt u(x,y) = 0?

6. Originally Posted by SoBeautiful
What is the E in part b? And doesnt u(x,y) = 0?
You are kidding. Are you not?