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December 3rd, 2016, 01:21 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, 01:29 PM   #2
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$f(z) = u(x,y) + i v(x,y)$

$\bar{f}(x) = u(x,y) +i (-v(x,y))$

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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