\(x + iy = \frac{(3+2i)(4-7i)(12 + 3i)}{(13 - 2i)(2 - 3i)(11 + 3i)}\)
\(= \frac{((12+14)+i(8 - 21))(12 + 3i)}{((26-6)-i(4+39))(11 + 3i)}\)
\(= \frac{(26 -13i) (12+3i)}{(20 - 43i) (11 + 3i)}\)
\(= \frac{351 - 78i}{349 - 413i}\)
\(= \frac{(351 - 78i) (349 + 413i)}{(349-413i) (349 + 413 i)}\)
\(= \frac{154713 + 117741i}{292370} = x + iy\)
\(\therefore x = \frac{154713}{292370}, y = \frac{117741}{292370}\)
\(x^2 + y^2 = \frac{37799055450}{85480216900} = 0.442\)
