Suppose u(x,y) and v(x,y) are harmonic on G and c is an element of R. Prove u(x,y) + cv(x,y) is also harmonic.(adsbygoogle = window.adsbygoogle || []).push({});

I tried using the Laplace Equation of Uxx+Uyy=0

I have:

du/dx=Ux

d^2u/dx^2=Uxx

du/dy=Uy

d^2u/dy^2=Uyy

dv/dx=cVx

d^2v/dx^2=cVxx

dv/dy=cVy

d^2v/dy^2=cVyy

I'm not really sure how to prove these are harmonic...am I missing a relationship?

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# I Complex Analysis Harmonic functions

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