Question

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

Answer 1

`2/(3+i) = 3/5-1/5i`

Explanation:

Multiply both numerator and denominator by the Complex conjugate `(3-i)` of the denominator and simplify:

`2/(3+i) = (2(3-i))/((3+i)(3-i)) = (2(3-i))/(3^2-i^2) = (2(3-i))/10 = (color(red)(cancel(color(black)(2)))(3-i))/(color(red)(cancel(color(black)(2)))*5) = 3/5-1/5i`