\[\frac{x - 1}{3 + i} + \frac{y - 1}{3 - i} = i\]
\[\frac{(x - 1)(3 - i) + (y - 1)(3 + i)}{(3 + i)(3 - i)} = i\]
\[\frac{3x - xi - 3 + i + 3y + yi - 3 - i}{9 + 1} = i\]
\[(3x + 3y - 6) + (y - x)i = 10i.\]
\[1)\ Действительная\ часть:\]
\[3x + 3y - 6 = 0\]
\[x + y - 2 = 0\]
\[y = 2 - x.\]
\[2)\ Мнимая\ часть:\]
\[y - x = 10\]
\[(2 - x) - x = 10\]
\[2x = - 8\]
\[x = - 4;\]
\[y = 2 + 4 = 6.\]
\[Ответ:\ \ x = - 4;\ y = 6.\]