Question

5i / 3-4i division of the following

Answer 1

`(5i)/(3 - 4i) = (3i - 4)/(5)`

Explanation:

Given

`(5i)/(3 - 4i)`

Required

Solve

We have:

`(5i)/(3 - 4i)`

Rationalize

`(5i)/(3 - 4i) = (5i)/(3 - 4i) * (3 + 4i)/(3 + 4i)`

`(5i)/(3 - 4i) = (5i(3 + 4i))/((3 - 4i)(3 + 4i))`

Apply difference of two squares on the denominator

`(5i)/(3 - 4i) = (5i(3 + 4i))/(3^2 - (4i)^2)`

`(5i)/(3 - 4i) = (5i(3 + 4i))/(9 - (16*-1))`

`(5i)/(3 - 4i) = (5i(3 + 4i))/(9 +16)`

`(5i)/(3 - 4i) = (5i(3 + 4i))/(25)`

Divide common factor (5)

`(5i)/(3 - 4i) = (i(3 + 4i))/(5)`

Expand the numerator

`(5i)/(3 - 4i) = (3i + 4*-1)/(5)`

`(5i)/(3 - 4i) = (3i - 4)/(5)`