Question

Please answer the attached question and chose from the provided options.

Answer 1

Option A
`-(19)/(74)+(71)/(74)i`

Explanation:

we know that

To divide complex numbers, you must multiply by the conjugate.

we have

`(-8+3i)/(5+7i)`

To find the conjugate, change the sign between the two terms in the denominator

so

`(-8+3i)/(5+7i)((5-7i)/(5-7i))=(-40+56i+15i-21i^(2))/(25-49i^(2)) \\\\=(-40+71i-21(-1))/(25-49(-1)) \\\\=(-19+71i)/(74)\\\\=-(19)/(74)+(71)/(74)i`