Các số thực x , y thỏa mãn sau (dfrac{{x – 3}}{{3 + i}} + dfrac{{y – 3}}{{3 – i}} = i). Khi đó tổng T = x + y bằng :

(begin{array}{l}dfrac{{x – 3}}{{3 + i}} + dfrac{{y – 3}}{{3 – i}} = i\ Leftrightarrow left( {x – 3} right)left( {3 – i} right) + left( {y – 3} right)left( {3 + i} right) = ileft( {3 – i} right)left( {3 + i} right)\ Leftrightarrow 3left( {x – 3} right) – left( {x – 3} right)i + 3left( {y – 3} right) + left( {y – 3} right)i = 10i\ Leftrightarrow 3left( {x + y – 6} right) + left( {y – x} right)i = 10i\ Leftrightarrow left{ begin{array}{l}x + y – 6 = 0\y – x = 10end{array} right.\ Leftrightarrow left{ begin{array}{l}x + y = 6\y – x = 10end{array} right.end{array})