Question

How do you divide `(1+i)/i - 3/(4-i)`?

Answer 1

I found: `5/17-20/17i`

Explanation:

To evaluate both fractions you first need to change the denominator into a pure real (manipulating the entire fraction). I would multiply and divide both fractions by a "good" complex number, as for example:
`(1+i)/i*color(red)(-i)/color(red)(-i)-3/(4-i)*(color(blue)(4+i))/(color(blue)(4+i))=`
`=(1-i)/1-(12+3i)/17=(17-17i-12-3i)/17=`
`=5/17-20/17i`