j is a term to indicate that the quantity has a direction that is at right angles to a quantity you can measure. It comes from J squared = -1 . if you have a sine wave and you multiply it by -1, its the same amplitude, but when the sinewave was + its now -, so j X the sinewave means the sinewave is at 90 degrees to the original. There are special rules for the j operator which you will have to learn, such as dividing by a j term, what you have to do is to multiply, top and bottom by -j, so the j on the bottom line becomes - j X j or 1, so it can be ignored.
In general, the voltage at the half way point on one leg is, Vin X (Zbottom/(Z top + Zbottom)), this occurs with the other leg, call it Vin X (Zbottom2/(Ztop2 + Zbottom2)). The voltage out is then the difference between the two, which is what you have.
Frank