Question

Alternativas:
A) √26 / 3
B) √26 / 5
C) √26
D) √26 / 2

Por favor, me ajudem! ✩

Answer 1

Resposta:

D

Explicação passo-a-passo:

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

Multiplicando pelo conjugado:

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

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

$z=\dfrac{3-5i-2}{1+1}$

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

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

Assim:

$|z|=\sqrt{\left(\dfrac{1}{2}\right)^2+\left(-\dfrac{5}{2}\right)^2}$

$|z|=\sqrt{\dfrac{1}{4}+\dfrac{25}{4}}$

$|z|=\sqrt{\dfrac{26}{4}}$

$|z|=\dfrac{\sqrt{26}}{2}$

Letra D