Question

2)dados os números complexos z¹=-7+5I e z²=3+2I,determine: a)z¹+z² b)z¹×z² c) z¹/z²​

Answer 1

Resposta: a) – 4 + 7i, b) – 31 + i, c) – 11/13 + 29i/13, d) 3 – 2i.

Lembrando que i² = – 1 e que z̅ é o conjugado de z, que tem sua parte real igual e sua parte imaginária simétrica.

a)

$z_1+z_2$

$=~~(-\,7+5i)+(3+2i)$

$=~~-7+5i+3+2i$

$=~~-4+7i$

b)

$z_1\times z_2$

$=~~(-\,7+5i)\times(3+2i)$

$=~~(-\,7)\times3+(-\,7)\times2i+5i\times3+5i\times2i$

$=~~-21-14i+15i+10i^2$

$=~~-21+i+10\times(-\,1)$

$=~~-21+i-10$

$=~~-31+i$

c)

$\dfrac{z_1}{z_2}$

$=~~\dfrac{-\,7+5i}{3+2i}$ ⇒ multiplique a fração toda pelo conjugado do denominador.

$=~~\dfrac{-\,7+5i}{3+2i}\times\dfrac{3-2i}{3-2i}$

$=~~\dfrac{(-\,7+5i)\times(3-2i)}{(3+2i)\times(3-2i)}$

$=~~\dfrac{(-\,7)\times3+(-\,7)\times(-\,2i)+5i\times3+5i\times(-\,2i)}{3^2-(2i)^2}$

$=~~\dfrac{-\,21+14i+15i-10i^2}{9-4i^2}$

$=~~\dfrac{-\,21+14i+15i-10\times(-\,1)}{9-4\times(-\,1)}$

$=~~\dfrac{-\,21+14i+15i+10}{9+4}$

$=~~\dfrac{-\,11+29i}{13}$

$=~~-\dfrac{11}{13}+\dfrac{29i}{13}$

d)

$\overline{z_2}$

$=~~3-2i$

Bons estudos e um forte abraço. — lordCzarnian9635.