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

1. ## 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'.

2. 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.

3. 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?

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