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

asked Sep 25, 2022 74.1k views

5 votes

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

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3 votes

Answer:

C. 8/25 - 19/25i

Explanation:

Given that:

(4-i)/(3+4i)

= ((4-i) (3-4i))/((3+4i)(3-4i))

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

=(8)/(25)- (19i)/(25)

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