Evaluate the limit if it exists $$f(z)=\begin{cases}1+z^2 & \text{if }z\not=i \\ 4i & \text{if }z=i \end{cases}$$
i.) evaluate limit as $z$ approaches $i$ if it exists
ii.) evaluate the limit as $z$ approaches $-i$ if it exists
iii.) where is $f(z)$ continuous? give a complete explanation
Sorry i am not familiar with the formatting. Can someone help me solve this problem and explain it in layman's terms?
my attempt at the solution:
converting $f(z)$ to $f(x+iy)$ and then finding the limit of $u(x,y)$ and $v(x,y)$?

You know, that the function $g(z)=1+z^2$ is continuous. Thus you can say $$\lim_{z\rightarrow i, z \neq i} f(z) = \lim_{z\rightarrow i, z \neq i} 1+ z^2 = 1+\left(\lim_{z\rightarrow i, z \neq i} z\right)^2 = 1+i^2 = 0$$
You can compute the limit for $z\rightarrow-i$ in the same way...
