How to solve number 11a on the pretest

Here is what i did to solve this problem:
First make z = a + bi and w = c + di.
Second, use the distance formula using these two points to get sqrt((a-c)^2+((b-d)*i)^2)
This is the true distance between the points.
Now, do abs(z-w). What this means is the distance from the origin after subtracting these two points. After subtracting them you get a+bi-c-di, or (a-c)+(b-d)i. Simply use the distance formula here to find the distance from zero to get the equation sqrt((a-c)^2+((b-d)*i)^2), which is identical to the equation found when using the distance formula of the two points directly.

I hope that helped... if not ask me to clarify please.