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December 3rd, 2016, 01:21 PM  #1 
Newbie Joined: Dec 2016 From: London Posts: 4 Thanks: 0  Complex Differentiable
Hi guys im stuck on this question, if anyone could help me out it would help a lot. Thanks.

December 3rd, 2016, 01:29 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,653 Thanks: 840 
$f(z) = u(x,y) + i v(x,y)$ $\bar{f}(x) = u(x,y) +i (v(x,y))$ Looking at the CR equations for each $\dfrac{\partial u}{\partial x} = \dfrac{\partial v}{\partial y}$ $\dfrac{\partial u}{\partial y}=\dfrac{\partial v}{\partial x}$ $\dfrac{\partial u}{\partial x}=\dfrac{\partial v}{\partial y}$ $\dfrac{\partial u}{\partial y}= \dfrac{\partial v}{\partial x}$ The only way these can all be true is if all the partials are equal to $0$ and thus both $f(z)$ and $\bar{f}(z)$ are both constant. 

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analysis, complex, differentaible, differentiable 
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