The correct choice is (c) Neither continuous nor differentiable
The explanation: z=x+iy
In general the limits are discussed at origin, if nothing is specified.
f(x, y)=\(\frac{x+iy+ix+i^2y}{(x+iy)^2}\)
f(x, y)=\(\frac{i(x+y)+(x-y)}{(x+iy)^2}\)
Left limit: \(\lim_{x \to 0 \\ y \to 0}\frac{i(x+y)+(x-y)}{(x+iy)^2}\)
\(\lim_{y \to 0}\frac{i(y)+(-y)}{(iy)^2}\)
=does not exist
Since, the left limit itself does not exist, the function is not continuous. If a function is not continuous, it cannot be differentiable as well.