Question

Efetue As Divisões Dos Numeros complexos
A) 3+i
___
2-3i

B) 3-7i
___
3+4i

Answer 1

a)

$\frac{3 + i}{2 - 3i} = \frac{(3 + i)(2 + 3i)}{(2 - 3i)(2 + 3i)} = \frac{6 + 9i + 2i + 3 {i}^{2} }{4 - 9i^{2} } = \frac{6 + 11i + 3 \times ( - 1)}{4 - 9 \times ( - 1)} = \frac{6 - 3 + 11i}{4 + 9} = \frac{3 + 11i}{13} = \frac{3}{13} + \frac{11i}{13}$

b)

$\frac{3 - 7i}{3 + 4i} = \frac{(3 - 7i)(3 - 4i)}{(3 + 4i)(3 - 4i)} = \frac{9 - 12i - 21i + 28 {i}^{2} }{9 - 16 {i}^{2} } = \frac{9 - 33i + 28 \times ( - 1)}{9 - 16 \times ( - 1)} = \frac{9 - 28 - 33i}{9 + 16} = \frac{ - 19 - 33i}{25} = - \frac{19}{25} - \frac{33i}{25}$

Answer 2

Resposta:

A)

3+i        2 +3i

___   x ______

2-3i       2+3i

(3+i)*(2+3i)/(4-9i²)

(6+9i+2i-3)/(4+9)

(3+11i)/13

B)

3-7i        3-4i

___     x _____

3+4i        3-4i

=(3-7i)*(3-4i) /(9-16i²)

=(9-12i-21i+28i²)/(19+16)

=(9-33i-28)/25

=(-19-33i)/25