Complex analysis: Show limit of complex function does not exist.

Hi there,

I was hoping someone could help me with this one.

I have a function of a complex variable, and I'm trying that the function is not differentiable at 0. i.e. f ' (0) does not exist.

I know I need to show that the limit does not exist at this point but I'm getting nowhere I'm afraid.

The function is as follows:



by conj. of z I mean the complex conjugate.

Any help you can give will be much appreciated.

Thank you,

Wayne.

Quote:

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Originally Posted by waynex

Hi there,

I was hoping someone could help me with this one.

I have a function of a complex variable, and I'm trying that the function is not differentiable at 0. i.e. f ' (0) does not exist.

I know I need to show that the limit does not exist at this point but I'm getting nowhere I'm afraid.

The function is as follows:



by conj. of z I mean the complex conjugate.

Any help you can give will be much appreciated.

Thank you,

Wayne.

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Use different paths and see what you get.