The limit of the complex conjugate as z -> 0

1. Oct 1, 2009

skriabin

Hi I'm wondering if the z- (complex conjugate of z) goes to zero as z does? Also what is the derivative of z- with respect to z? Thanks

2. Oct 2, 2009

skriabin

This is very important for me right now, so please if you know this, let me know... :)

3. Oct 2, 2009

Office_Shredder

Staff Emeritus
The map f(z)= conjugate of z is not differentiable, and you should be able to prove this from the definition.

Do you know how to calculate complex limits by breaking them up into their real and imaginary parts? It makes looking at that limit very easy

4. Oct 3, 2009

skriabin

Thank you. Got it.

5. Oct 3, 2009

AxiomOfChoice

While we're on the subject of complex limits, can anyone help me figure out what
$$\lim_{z\to 0} \text{Log } z$$
is? (So we're talking about the principal logarithm here.)