a)

Find the deriviative of the following function and specify the domain of this derviative

f(z)=[Log(4z-i)]/z^2

b)

Use the defintion of the derivative to prove that the function

f(z)=Im z -2i

is not differentiable at 1+2i

a)

Now I have attempted this question using the quotient Rule and ended up with something like this

f'(z)=[z^2(4/4z-i)-(2z)Log(4z-i)](z^2)^2

=[4z^2/(4z-i)-2zLog(4z-i)]/z^4

Now i am not sure on how to simplfy it further. The value thats getting to me is the most is the 4z^2/(4z-i)/z^4. Hope fully some one can show me how to do it and also help on what the domain is.

b)

For this part i know i am to use the formula

[f(z)-f(a)]/z-a

But how to do it is really confusing. I think as well that the Imz part is making it probably seem harder then it actually is.

Hopefully someone can point me in the right direction

Thanx

Bex