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December 3rd, 2016, 12:21 PM   #1
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Complex Differentiable

Hi guys im stuck on this question, if anyone could help me out it would help a lot. Thanks.
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 December 3rd, 2016, 12:29 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,100 Thanks: 1093 $f(z) = u(x,y) + i v(x,y)$ $\bar{f}(x) = u(x,y) +i (-v(x,y))$ 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. Thanks from Haz5069

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