Question

Divide the following complex numbers:
(4-i)/(3+4i)
A.-8/7 + 19/7i
B. 16/25 - 19/25i
C. 8/25 - 19/25i
D. -16/7 + 19/7i

Answer 1

Answer:

C. 8/25 - 19/25i

Step-by-step explanation:

Given that:

$\dfrac{4-i}{3+4i}$

$= \dfrac{(4-i) (3-4i)}{(3+4i)(3-4i)}$

$= \dfrac{(4-i) (3-4i)}{(3+4i)(3-4i)} \\ \\ =\dfrac{12 -16i -3i+4i^2}{9 - 12i +12i -16i^2} \\ \\ = \dfrac{12-19i+4i^2}{9-16i^2} \\ \\ = \dfrac{8-19i}{25}$

$=\dfrac{8}{25}- \dfrac{19i}{25}$