\(\frac {a+bi+2} {b+ai-2}= 3 \)  ⇔  a + bi + 2 = 3b + 3ai − 6  ⇔  (a+2) + bi = (3b − 6) + 3ai
      \(\small \Leftrightarrow \left\{\begin{matrix}a+2=3b-6\\b=3a\end{matrix}\right. \Leftrightarrow \left\{\begin{matrix}a=9a-8\\b=3a\end{matrix}\right. \Leftrightarrow \left\{\begin{matrix}8=8a \\b=3a\end{matrix}\right. \Leftrightarrow \left\{\begin{matrix}a=1 \\b=3 \end{matrix}\right.\)
Dus :   a + b = 1 + 3 = 4