Question

2) Calcule a divisão de 2 + 3.i por 1 - 1.i .

Alguém poderia me ajudar, pfvvvv​

Answer 1

Explicação passo-a-passo:

$z=\dfrac{2+3i}{1-i}$

Multiplicando o numerador e o denominador pelo conjugado de 1-i, ou seja,

1+i.

$z=\dfrac{2+3i}{1-i}.\dfrac{1+i}{1+i} \\\\\\z=\dfrac{2.1+2.i+3i.1+3i.i}{1.1+1.i-i.1-i.i} \\\\\\z=\dfrac{2+2i+3i+3i^{2} }{1+i-i-i^{2} } \\\\\\\z=\dfrac{2+5i+3.(-1)}{1-(-1)} \\\\\\z=\dfrac{2-3+5i}{2} \\\\\\z=\dfrac{-1+5i}{2}\\\\\\\boxed{\boxed{z=\dfrac{-1}{2} +\dfrac{5}{2}i }}$