Question

How do you divide `3/(5i)`?

Answer 1

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

Explanation:

Keep in mind that `i=sqrt(-1)` which means that `i^2=-1` and therefore `i^4=1`. So we can rewrite the question as:

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

`i^3=-sqrt(-1)=-i` and so:

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

Answer 2

`-3/5i`

Explanation:

To divide this fraction we require the denominator to be a real number.

This is achieved in this case by multiplying the numerator/denominator by i.

`rArr3/(5i)=3/(5i)xxi/i=(3i)/(5i^2)`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(i^2=(sqrt(-1))^2=-1)color(white)(a/a)|)))`

`rArr(3i)/(5i^2)=(3i)/(-5)=-3/5i`