Question

How do you divide `(4+i)/(8i)`?

Answer 1

`1/8-1/2i`

Explanation:

To divide this fraction we require the denominator to be a `color(blue)"real number "`and not a `color(blue)"complex number"` as it is.

To achieve this multiply the numerator and denominator . in this case by i.

Since: `8ixxi=8i^2=-8larr" a real number"`

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

Since this is a fraction, we must also multiply the numerator by i.

`rArr(i(4+i))/(8i^2)=(4i-1)/(-8)`

divide each term on the numerator by - 8

`rArr(4i)/(-8)-1/(-8)=1/8-1/2i" in standard form"`