Question 22
The solutions to the equations $z^2 = 4 + 4\sqrt{15}\,i$ and $z^2 = 2 + 2\sqrt{3}\,i,$ where $i = \sqrt{-1},$ form the vertices of a parallelogram in the complex plane. The area of this parallelogram can be written in the form $p\sqrt{q} - r\sqrt{s},$ where $p,$ $q,$ $r,$ and $s$ are positive integers and neither $q$ nor $s$ is divisible by the square of any prime number. What is $p + q + r + s?$