Question

(UEM-PR) A forma algébrica do número complexo 11 + 2i/2-i é:
a) -4/3 + 3/2i
b) 13 + 13i
c) 3+3i
d)4+3i
e) 1/2+i/2

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo-a-passo:

$\mathsf{\dfrac{11 + 2i}{2 - i} \times \dfrac{2 + i}{2 + i} = \dfrac{22 + 11i + 4i + 2i^2}{4 + 2i - 2i - i^2}}$

$\mathsf{\dfrac{22 + 11i + 4i + 2i^2}{4 + 2i - 2i - i^2} = \dfrac{22 + 11i + 4i + 2(-1)}{4 + 2i - 2i - (-1)}}$

$\mathsf{\dfrac{22 + 11i + 4i + 2(-1)}{4 + 2i - 2i - (-1)} = \dfrac{22+ 11i + 4i - 2}{4 + 2i - 2i + 1}}$

$\mathsf{\dfrac{20+ 15i}{5} = 4 + 3i}$

$\boxed{\boxed{\mathsf{\dfrac{11 + 2i}{2 - i} = 4 + 3i}}}\leftarrow\textsf{letra D}$