Question

efetuando -se a operação 2 + i / -3 + i , obtém -se:

Answer 1

$\dfrac{2+i}{-3+i}\longrightarrow\dfrac{2+i}{i-3}\longrightarrow\dfrac{2+i}{i-3}\cdot\dfrac{i+3}{i+3}\longrightarrow\\\\\\\dfrac{2i+6+i^2+3i}{i^2-9}\longrightarrow\dfrac{i^2+5i+6}{i^2-9}\longrightarrow\dfrac{(-1)+5i+6}{(-1)-9}\longrightarrow\\\\\\\dfrac{5i+5}{-10}\longrightarrow\boxed{\boxed{-\dfrac{i+1}{2}}}$