(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

write down the C-R equations and use them to determine those points at which the following functions are analytic

(i)h(z)=[itex]x^2-y^2-x + i(2xy+y) [/itex]

(ii)h(z)=cos2xcosh2y - isin2xsinh2y

2. Relevant equations

3. The attempt at a solution

ok so C-R equations are for z=u+iv eq1 = [itex] \frac{\partial u}{\partial x} = \frac{\partial v}{\partial y} [/itex] and eq2= [itex] \frac{\partial u}{\partial y} = - \frac{\partial v}{\partial x} [/itex]

for for (i) i get [itex]\frac{\partial u}{\partial x} = 2x-1 and \frac{\partial v}{\partial y} = 2x+1 [/itex]

and [itex]\frac{\partial v}{\partial x} = 2y and \frac{\partial u}{\partial y} = -2y [/itex] equation 2 holds but equation 1 does not hold. So am i right in thinking the function is not analytic? both equations have to be satisfied right? its the way the question is worded is throwing me "those points" ...

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Cauchy-Riemann equations

**Physics Forums | Science Articles, Homework Help, Discussion**