
Complex Analysis Complex Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
December 3rd, 2016, 12:21 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, 12:29 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,388 Thanks: 1288 
$f(z) = u(x,y) + i v(x,y)$ $\bar{f}(x) = u(x,y) +i (v(x,y))$ 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. 

Tags 
analysis, complex, differentaible, differentiable 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
is this differentiable?  Omnipotent  Calculus  0  October 4th, 2014 01:46 PM 
Limits of a differentiable f(x)  bobcantor1983  Calculus  6  October 1st, 2013 02:16 PM 
differentiable at x_0  alphabeta89  Real Analysis  4  January 28th, 2012 01:56 AM 
differentiable at x_0  alphabeta89  Real Analysis  0  January 18th, 2012 02:52 AM 
Is f differentiable  SyNtHeSiS  Calculus  2  April 29th, 2010 03:08 PM 