Question

Write the complex number `(-5 - 3i)/(4i)` in standard form?

Answer 1

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

Explanation:

We want the complex number in the form `a+bi`. This is a bit tricky because we have an imaginary part in the denominator, and we can't divide a real number by an imaginary number.

We can however solve this using a little trick. If we multiply both top and bottom by `i`, we can get a real number in the bottom:

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

Answer 2

`-3/4+5/4i`

Explanation:

`color(orange)"Reminder"color(white)(x)i^2=(sqrt(-1))^2=-1`

`"multiply numerator/denominator by "4i`

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

`=(-20i-12i^2)/(16i^2)`

`=(12-20i)/(-16)`

`=12/(-16)-(20i)/(-16)`

`=-3/4+5/4ilarrcolor(red)"in standard form"`