Proving Analyticity of u_x - iu_y in Complex Analysis

[bballife1508]

Suppose that u(x,y) is harmonic for all (x,y). Show that u_x-iu_y is analytic for all z.

(Assume that all derivatives in the question exist and are continuous)

I have no idea where to start with this? Something with the Cauchy Riemann equations is required but I'm not sure exactly how to incorporate them.

 

[╔(σ_σ)╝]

Look up what it means to be harmonic ( Hint: It involves second partial derievatives).

Then you cauchy riemann equations to write the form of your derievative of u_x - iu_y. Relate the two ideas.

 

[bballife1508]

i'm aware of what harmonic is. the second partials of u add to 0, but how do i relate this to the C.R equations

 

[╔(σ_σ)╝]

What are the cauchy riemann equations ? Can you write them out ?

 

[gomunkul51]

Write down the definition of a Harmonic Function, write down the C-R equations.
now can you manipulate them to get what is needed?
(HINT: try integration and differentiation).