Complex Analysis Complex Analysis Math Forum

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.
Attached Images Untitled.jpg (9.2 KB, 5 views) December 3rd, 2016, 01:29 PM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,628 Thanks: 1469 $f(z) = u(x,y) + i v(x,y)$ $\bar{f}(x) = u(x,y) +i (-v(x,y))$ 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 Tags analysis, complex, differentaible, differentiable Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Omnipotent Calculus 0 October 4th, 2014 02:46 PM bobcantor1983 Calculus 6 October 1st, 2013 03:16 PM alphabeta89 Real Analysis 4 January 28th, 2012 02:56 AM alphabeta89 Real Analysis 0 January 18th, 2012 03:52 AM SyNtHeSiS Calculus 2 April 29th, 2010 04:08 PM

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