I'm wondering about the logistics of this problem in picrel; specifically about parts (a), (b), and (c).

For part (a), the answer is [(q*az)/(4*pi*e0*z^2)] * [(1 - d/2z)^-2 - (1 + d/2z)^-2] (Tell me if you need a pic of that written out on paper)

I have gotten a similar answer using the superposition theorem for electromagnetic intensity, but without the z^2 on the bottom or the 2z as the denominator of the d-expressions. And I'm just wondering how the answer for (a) evaluates to this.

I am also wondering how (b) in the case of evaluating z at (0, 0, 0) does not become zero.

Last, for part (c), I am wondering how to get the horizontal and vertical components for this. I don't want to be hand-fed this part-- I just want to understand how it works so I can solve it myself because I am working through similar problems that ask me to evaluate electric fields of various types on the XY plane.

I am sure there's a few pieces I'm missing from the puzzle, but I want to understand how the answers evaluate to how they are.