Register to reply 
Z (conjugate) not analytic? 
Share this thread: 
#1
Oct2411, 10:12 PM

P: 33

1. The problem statement, all variables and given/known data
Show that f(z) = ¯z is not differentiable for any z ∈ C. 2. Relevant equations 3. The attempt at a solution Is it because the CauchyReimann Equations don't hold? Z (conjugate) = xiy u(x,y)=x v(x,y=iy du/dx=1≠dv/dy=1 du/dy=0≠dv/dx=0 Edit: Is there another approach? Because the CR Equations is something we learned later on. 


#2
Oct2411, 10:24 PM

Sci Advisor
HW Helper
Thanks
P: 25,228




#3
Oct2411, 10:41 PM

P: 33

I think I get it now.
(f(z+h)f(z))/h (conjugate((z+h)z))/h = h(conjugate)/h If h=Δx, the ratio equals 1 If h=Δiy, the ratio equals 1. Since the two approaches don't agree for any z, z(conj) is not analytic anywhere. Correct? 


#4
Oct2411, 10:51 PM

Sci Advisor
HW Helper
Thanks
P: 25,228

Z (conjugate) not analytic?



Register to reply 
Related Discussions  
Prove a nonvanishing analytic function on a convex set has form e^(g(z)), g analytic  Calculus & Beyond Homework  3  
Quaternions, how to prove q^** = q  Calculus & Beyond Homework  3  
Conjugate of e^(iz)  Calculus & Beyond Homework  7  
Conjugate of either sin or cos  Electrical Engineering  1  
Conjugate pairs versus not conjugate pairs  Chemistry  1 