Then I would have to ask why are you using imaginary numbers as lengths?

Cheers,
Swiftless

That is exactly true, A^2 + B^2 will only equal 0 if A and B is 0.

While the formula you have given is the true formula for working out the distance between two points, look at what it is actually doing. I will look at 2D space:

Now if we have a collision when the result is 0, if we apply some basic maths to the distance formula, we can remove the sqrt:
0 = sqrt((x2-x1)^2 + (y2-y1)^2)
0^2 = sqrt((x2 – x1)^2 + (y2 – y1)^2)^2
0 = (x2 – x1)^2 + (y2 – y1)^2

And now look at what x2-x1 and y2-y1 do. They give us the length of the line segments A and B.

Therefore:
x2 – x1 = A and y2 – y1 = B
And then:
0 = (A)^2 + (B)^2
0 = A^2 + B^2

Therefore we have a collision. Both this shorthand version and the full version of the distance formula are the same thing.

Hope this helps clarify
Swiftless