Alan

.As Melody often notes, it can be useful to plot these sort of probabilities against each other.  Consider x_1 and x_2:

The probabilities of the pair can be thought of as uniformly randomly scattered points within a unit square.

The only regions of the square in which the lengths between the two values are greater than 3/4, are within the two red triangles indicated in the image above.

The probability that the lengths are greater than 3/4 is therefore given by p = Area of triangles/Area of square

The same probability holds for the lengths between x_3 and x_4, so, because the two probabilities are independent, the overall probability is given by p^2.

I'll leave you to do the number crunching.

You need to specify what you mean by "practical" domain.  The mathematical domain is -infinity to +infinity, so your use of "practical" suggests you have some limits on the values of V(x) (which we don't know).

@ bingboy

There's a sign wrong here:  (3x + 4y) + (3y - 4x)i = 1 - 8i

Hmm.  Look at the following:

Some checking is in order bingboy!

See if this helps:

Look at the diagram:

Find angle $\alpha$ using the cosine rule    (i.e. $cos(a) = (b^2 + c^2 - a^2)/(2bc)$ )

Take the ratio of the arc of the circle subtended by $2\alpha$  to that of the circumference of the whole circle to get the probability.

i.e. probability = $2\alpha / (2\pi)$

(Note that the lower point could be on the opposite side of the circle hence $2\alpha$ not just $\alpha$)

Like this (assuming my simplification of the numbers is correct):

I'll leave you to solve the above to find the actual value of Cfixed.

Hmm!  Check the left-hand side of 15f = 5m

As follows:

The following is one possibility: