Question

Sendo a= 3 + 2i e b = 1 + i, obter a:b

Escolha uma:
a) 5 – 0,5 i
b) 2,5 + 0,5 i
c) – 0,5 i
d) 5 + 0,5 i
e) 2,5 – 0,5 i

Answer 1

Resposta:

E

Explicação passo-a-passo:

$\dfrac{a}{b}=\dfrac{3+2i}{1+i}$

$\dfrac{a}{b}=\dfrac{3+2i}{1+i}\cdot\dfrac{1-i}{1-i}$

$\dfrac{a}{b}=\dfrac{3+2i-3i-2i^2}{1^2-i^2}$

$\dfrac{a}{b}=\dfrac{3+2i-3i-2\cdot(-1)}{1-(-1)}$

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

$\dfrac{a}{b}=\dfrac{5-i}{2}$

$\dfrac{a}{b}=\dfrac{5}{2}-\dfrac{i}{2}$

$\dfrac{a}{b}=2,5-0,5i$

Letra E

Answer 2

$\dfrac{3 + 2i}{1 + i}$

$\dfrac{(3+2i)\times(1-i)}{(1 + i)\times(1-i)}$

$\dfrac{3 - 3i + 2i - 2 {i}^{2} }{1 - {i}^{2} }$

$\dfrac{3 - i - 2 \times ( - 1)}{1 - (- 1)}$

$\dfrac{3 + 2 - i}{2}$

$\dfrac{5 - i}{2} = \dfrac{5}{2} - \dfrac{1}{2} i$

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Alternativa : E) 2.5 - 0.5i.

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Espero Ter Ajudado !!