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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Originally Posted by jackjack123 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.
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?
I think it'd simply be differentiable everywhere in the complex plane except when z = i, i.e. C \ {i} ?
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