My Math Forum Complex Differentiable

 Complex Analysis Complex Analysis Math Forum

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.
Attached Images
 Untitled.jpg (9.2 KB, 5 views)

 December 3rd, 2016, 12:29 PM #2 Senior Member     Joined: Sep 2015 From: Southern California, USA Posts: 1,481 Thanks: 744 $f(z) = u(x,y) + i v(x,y)$ $\bar{f}(x) = u(x,y) +i (-v(x,y))$ 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

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Omnipotent Calculus 0 October 4th, 2014 01:46 PM bobcantor1983 Calculus 6 October 1st, 2013 02:16 PM alphabeta89 Real Analysis 4 January 28th, 2012 01:56 AM alphabeta89 Real Analysis 0 January 18th, 2012 02:52 AM SyNtHeSiS Calculus 2 April 29th, 2010 03:08 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top