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Z (conjugate) not analytic? 
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#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

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#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

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Z (conjugate) not analytic?



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