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Math Help - Help With determining points in complex plane when differentiable

  1. #1
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    Help With determining points in complex plane when differentiable

    I'm having trouble with this problem here.

    Determine all the points in the complex plane where the functions

    f(z) = (z + 1)/(z - i)

    are differentiable and find the formulas for the derivative f'.
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  2. #2
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    Quote Originally Posted by jackjack123 View Post
    I'm having trouble with this problem here.

    Determine all the points in the complex plane where the functions

    f(z) = (z + 1)/(z - i)

    are differentiable and find the formulas for the derivative f'.
    Just do the derivative using the usual quotient rule you learned in
    Calculus I. And it should be obvious that f is differentiable for all z except i.
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  3. #3
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    what would the first step be? would multiply each side by (z+1)/(z+1) or would you have to replace the each z by x + y.i ?

    and then do quotient rule?
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  4. #4
    Junior Member enjam's Avatar
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    I think it'd simply be differentiable everywhere in the complex plane except when z = i, i.e. C \ {i} ?
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