Question

How do you simplify `(3+9i)/(3i)`?

Answer 1

`(3+9i)/(3i)=(cancel(3)(1+3i))/((cancel3)i)=(1+3i)/i=(1+3i)/i xxi/i=(i+3i^2)/i^2=(i-3)/-1=3-i`.

Explanation:

Alternatively, `(3+9i)/(3i)=3/(3i)+(9i)/(3i)=1/i+3={(1*i)/(i*i)}+3`

`=i/i^2+3=i/-1+3=3-i`.