Question

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

Answer 1

Multiply the numerator and denominator by the conjugate of the denominator to find that
`(2+i)/(3+i) = 7/10 + 1/10i`

Explanation:

The conjugate of a complex number `a+bi` is `a-bi`. The product of a complex number and its conjugate is a real number. Using that, we get

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

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

`= (7 + i)/10`

`= 7/10 + 1/10i`