Question

Calcule:
a) (8 – 2i) . (4 + 5i)
b) (6 + i) . (6 – i)
c) 6 -6i/ 7 +8i
D) 2 + 3i/ 5 + 7i

Answer 1

Explicação passo-a-passo:

a)

(8 – 2i) . (4 + 5i) =

8.4 + 8.5i - 2i.4 - 2i.5i =

32 + 40i - 8i - 10i^2 =

32 + 32i - 10(-1) =

32 + 32i + 10 =

42 + 32i

b)

(6 + i).(6 - i) =

(6)^2 - i^2 =

36 - 1 =

35

c)

$\frac{6-6i}{7+8i}=</p><p>\frac{(6-6i).(7-8i)}{(7+8i).(7-8i)}=</p><p>\frac{6.7-6.8i-6i.7+6i.8i}{7^{2}-(8i)^{2}}=</p><p>\frac{42-48i-42i+48i^{2}}{49-64.(-1)}=</p><p>\frac{42-90i+48.(-1)}{49+64}=</p><p>\frac{42-48-90i}{113}=</p><p>\frac{-6-90i}{113}=</p><p>\frac{-6}{113}-\frac{90i}{113}$

d)

$\frac{2+3i}{5+7i}=</p><p>\frac{(2+3i)(5-7i)}{(5+7i)(5-7i)}=</p><p>\frac{2.5-2.7i+3i.5-3i.7i}{(5)^{2}-(7i)^{2}}=</p><p>\frac{10-14i+15i-21i^{2}}{25-49(-1)}=</p><p>\frac{10+i-21.(-1)}{25+49}=</p><p>\frac{10+i+21}{74}=</p><p>\frac{31+i}{74}=</p><p>\frac{31}{74}+\frac{i}{74}$