Question: Find the limit of the function at the given point or explain why it does not exist.
f(z)=(z3-8i)/(z+2i)
(zā -2i) at z0=-2i
Solution:
f(z)=(z3-8i)/(z+2i)
f(z)=(z3+(2i)3)/(z+2i)
f(z)=((z+2i)(z2-2iz+(2i)2)/(z+2i)
f(z)=(z+2i)(z2-2iz+(2i)2
limz ā -2i f(z) =limz ā -2i (z+2i)(z2-2iz+(2i)2
=(-2i)2-2i(-2i)+(2i)2=12i2=-12
