Question

Na divisão de números complexos responda: z = 4 - 7i w = 2 + 6i z/w *


a) 17 - 19i / 16

b) 34 + 38i / 32

c) 17 + 19i / 16

d) 18 + 19i / 16

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Answer 1

Resposta: Nenhuma Das Alternativas.

Se z = 4 – 7i e w = 2 + 6i, então o quociente entre z e w é:

$\sf\frac{z}{w}$

$\sf\frac{4\,-7i}{2\,+\,6i}$ ⇒ multiplique a fração pelo conjugado do denominador.

$\sf\frac{4\,-7i}{2\,+\,6i}\times\frac{2\,-\,6i}{2\,-\,6i}$

$\sf\frac{(4\,-7i)\,\times\,(2\,-\,6i)}{(2\,+\,6i)\,\times\,(2\,-\,6i)}$

$\sf\frac{8\,-\,24i\,-\,14i\,+\,42i^2}{2^2\,-\,6^2i^2}$

$\sf\frac{8\,-\,38i\,+\,42i^2}{4\,-\,36i^2}$ ⇒ sabe-se que i = √(– 1), então i² = – 1.

$\sf\frac{8\,-\,38i\,+\,42\,\times\,(-\,1)}{4\,-\,36\,\times\,(-\,1)}$

$\sf\frac{8\,-\,38i\,-\,42}{4\,+\,36}$

$\sf\frac{-\,34\,-\,38i}{40}$ ⇒ simplifique.

$\sf\frac{(-\,17\,-\,19i)\,\times\,2}{20\,\times\,2}$

$\sf\frac{-\,17\,-\,19i}{20}$

N.D.A.

Bons estudos e um forte abraço. — lordCzarnian9635.