Question

Dados os números complexos z = 2 + 2i e w = 4 + i, calcule: a) z. W b) z/w

Answer 1

Resposta:

Explicação passo a passo:

z = 2 + 2i

w = 4 + i

a) z . w = (2 + 2i)(4 + i)

   z , w = 8 + 2i + 8i + i²

   z . w = 8 + 10i - 1

   z . w = 9 + 10i

b)

$\frac{z}{w} =\frac{2+2i}{4+i} \times \frac{4-i}{4-i} \\\\\frac{z}{w} =\frac{8-2i+8i-2i^2}{4^2-i^2} \\\\\frac{z}{w} =\frac{8+6i+2}{16+1} \\\\\frac{z}{w} =\frac{10+6i}{17} \\\\\frac{z}{w} =\frac{10}{17} +\frac{6i}{17}$