Question

How do you simplify `(4+2i)/(3-i)`?

Answer 1

Multiply by the conjugate of the denominator to find that
`(4+2i)/(3-i)=1+i`

Explanation:

Given a complex number `a+bi`, the complex conjugate of that number is `a-bi`. A useful property is that the product of a complex number and its conjugate will be a real number. We will use that to eliminate the complex number from the denominator.

`(4+2i)/(3-i) = ((4+2i)(3+i))/((3-i)(3+i))`

`=(10+10i)/10`

`=1+i`