Question

use the definition to the derivative of : f(z)=(2z-i)/(z-2i) at z=-i .

Answer 1

.......of the derivative? or what...?

Answer 2

Writing down the difference quotient we talked about earlier

[f(z)-f(-i)]/(z+i)

we have

\[\frac{(2z-i)/(z-2i) - (-3i)/(-3i)}{z+i}\]

Answer 3

convince yourself that is correct, then simplify, and you'll find that taking the limit as z --> -i is easy.