Question

How do you simplify `(-2-5i)/(3i)`?

Answer 1

`-5/3+2/3i`

Explanation:

We require the denominator to be a real number. This can be achieved by multiplying the numerator/denominator by 3i.

`(-2-5i)/(3i)xx(3i)/(3i)=(-6i-15i^2)/(9i^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(-6i-15i^2)/(9i^2)=(15-6i)/(-9)`

and dividing.

`=15/(-9)+(-6)/(-9)i=-5/3+2/3i`