Suppose that x, y, and z are complex numbers such that x y=-80-320 i, y z=60, and z x=-96+24 i, where i=\sqrt{-1}. Then there are real numbers a and b such that x+y+z=a+b i. Find a^{2}+b^{2}.
Suppose that x, y, and z are complex numbers such that x y=-80-320 i, y z=60, and z x=-96+24 i, where i=\sqrt{-1}. Then there are real numbers a and b such that x+y+z=a+b i. Find a^{2}+b^{2}.