Question

plz help me in solving this prob.
discuss the continuity of the function.
f(z)={((z)4-(z)3+(z)2-(z)+1)/(z-i) ,z!=i
{iz ,z=i

Answer 1

if z=i, then f(z) = -1
if z!=i, using Lhopital theorem, differential den, num at the same time with respect to z, the \[f(z=i)=[4z^3-3z^2+2z-1]/1|_{(z=i)}=[-4i+3+2i-1]=2[-i+1]\]
is different from the above result when z=i
conclusion : this fn is not continuous at z=i