Question

Para as questões a seguir considere z1=3+2i z2=-1+i
O resultado de Z1/Z2.

Answer 1

Para realizar esta operação, vamos multiplicar numerador e denominador pelo conjugado do denominador, acompanhe:

$\dfrac{3+2i}{-1+i}~=~\\\\\\\\=~\dfrac{3+2i}{-1+i}~.~\dfrac{-1-i}{-1-i}\\\\\\\\=~\dfrac{3~.~(-1)~+~3~.~(-i)~+~2i~.~(-1)~+~2i~.~(-i)}{(-1)~.~(-1)~+~(-1)~.~(-i)~+~i~.~(-1)~+~i~.~(-i)}\\\\\\\\=~\dfrac{-3~-~3i~-~2i~-~2i^2}{1~+~i~-~i~-~i^2}\\\\\\\\=~\dfrac{-3~-~5i~-~2\,.\,(-1)}{1~-~(-1)}\\\\\\\\=~\boxed{\dfrac{-1~-~5i}{2}}~~ou~~\boxed{-\dfrac{1}{2}~-~\dfrac{5}{2}i}$