Question

Quotient of 1+i/3+4i?

Answer 1

7/25-1/25i

I took the iready test

Answer 2

`(7)/(25) - (1)/(25)i`

Explanation:

I assume you are asking

`(1 + i)/(3 + 4i)`

although what you wrote means this

`1 + (i)/(3) + 4i`

Back to what I think is your problem:

`(1 + i)/(3 + 4i) =`

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

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

`= (3 - 4i + 3i - 4i^2)/(9 - 16i^2)`

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

`= (7 - i)/(25)`

`= (7)/(25) - (1)/(25)i`