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Math Help - Show that a function is not differentiable anywhere...

  1. #1
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    Show that a function is not differentiable anywhere...

    Can anyone please help me with this question, I am really confused...

    Show that the function g(z)=Im z is not differentiable anywhere using the definition of f to be differentiable at a point 'z' . where f:u (tending to)Complex numbers.

    for f to be differentiable then the limit of
    lim [f(z) - f(z0)]/(z-z0) (z tending to z0) must exist. But how so I show that this is not the case with g(z)=Im z ...the imaginary part?

    Thanks
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  2. #2
    Junior Member
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    Aug 2010
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    In order for the complex derivative to exist, the differential quotient must be the same for any sequence approaching z_0.
    For g(z)=Im z you can find 2 complex sequences approaching z_0, for which the differential quotient is different.

    Take for example
    a_n:=z_0+i/n
    and b_n:=z_0+1/n
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