Question

How do you divide `(8i)/(-1+3i)`?

Answer 1

I found: `2.4-0.8i`

Explanation:

To perform this division between complex numbers we need first to transform the denominator into a Real number; to do that we can multiply and divide by the complex conjugate of the denominator:
`(8i)/(-1+3i)*color(red)((-1-3i)/(-1-3i))=((8i)(-1-3i))/((-1+3i)(-1-3i))=`
`=(-8i+24)/(1+9)=`
remembering that `i^2=-1`
Now we can perform the division having in the denominator a simple real number:
`=(24-8i)/10=24/10-8/10i=2.4-0.8i`