2012 AIME II Problem 8

The complex numbers z and w satisfy the system z + \frac{20i}w = 5+i w+\frac{12i}z = -4+10i Find the smallest possible value of \vert zw\vert^2.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.